messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1
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[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-3|(2|(-5((2(4x - 1) - 1)/(3(4x - 1) - 2))^2 - 1((2(4x - 1) - 1)/(3(4x - 1) - 2)) + 1) + 2| - 1)| + 1) - 1| and g(x) = -1|(1|(2((-1((3x + 2)/(-3x + 4)) + 3)/(2((3x + 2)/(-3x + 4)) + 2)) - 3) + 2| + 2) - 2| - 3 between the vertic... | 1.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -5(3|((-3(2cos(3π(2|(2x^2 + 5x - 3) + 3| + 1) - 1) - 1) + 2)/(2(2cos(3π(2|(2x^2 + 5x - 3) + 3| + 1) - 1) - 1))) - 2|) + 1 and g(x) = -1|(2|(3|(-3(-2cos(1πx - 3) - 3)^2 - 3(-2cos(1πx - 3) - 3) - 5) - 3| - 3) - 2| + 1) - 1| - 1 from x = -3.7 t... | 4.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(2(-1cos(2π(-4(5(-1|x + 3| + 3) - 5) - 4)) - 3)^2 + 3) - 2| + 2 and g(x) = 2e^(2(-2(-1(-4(-1|x + 1| + 2) - 5)^2 - 5(-4(-1|x + 1| + 2) - 5) - 1)^2 - 4(-1(-4(-1|x + 1| + 2) - 5)^2 - 5(-4(-1|x + 1| + 2) - 5) - 1))) - 1 between the ve... | 3.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(3cos(2π(4(-4(3(1x + 1)^2 + 1(1x + 1) - 4) + 4) + 2)) - 1) - 2| + 2 and g(x) = (2(-1((1(2e^(-1(2x - 5)) - 1) - 2)/(-1(2e^(-1(2x - 5)) - 1) - 2))) + 1)/(-3(-1((1(2e^(-1(2x - 5)) - 1) - 2)/(-1(2e^(-1(2x - 5)) - 1) - 2))) + 1) from x = 2.2 to... | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(3((-1((-2(4((-2x - 2)/(1x + 2)) + 3) - 1)/(-2(4((-2x - 2)/(1x + 2)) + 3))) - 3)/(2((-2(4((-2x - 2)/(1x + 2)) + 3) - 1)/(-2(4((-2x - 2)/(1x + 2)) + 3))) - 1))^2 - 5((-1((-2(4((-2x - 2)/(1x + 2)) + 3) - 1)/(-2(4((-2x - 2)/(1x + 2)) + 3))) -... | 4.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-3(-2(3(2|(4x + 4) - 2|) - 2)^2 - 1(3(2|(4x + 4) - 2|) - 2) - 1) - 3)/(1(-2(3(2|(4x + 4) - 2|) - 2)^2 - 1(3(2|(4x + 4) - 2|) - 2) - 1) + 2)) - 3 and g(x) = -5((3(-4(-2(-2x^2 + 2x + 4)^2 - 3(-2x^2 + 2x + 4) - 3)^2 + 4(-2(-2x^2 + ... | 3.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1|(3e^(-2(-1(2(2x - 1) - 5) - 4)) - 3) - 2| + 1) + 5 and g(x) = (-1((2(3(1sin(2π(1|x| + 1) - 2) - 3)^2 + 4(1sin(2π(1|x| + 1) - 2) - 3) - 4) - 1)/(-2(3(1sin(2π(1|x| + 1) - 2) - 3)^2 + 4(1sin(2π(1|x| + 1) - 2) - 3) - 4) + 3)))/(1(... | 5.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4((2((-2(3|(-2cos(3π((1x)/(2x + 3)) + 1) + 1) + 2|))/(1(3|(-2cos(3π((1x)/(2x + 3)) + 1) + 1) + 2|) + 1)) + 2)/(-1((-2(3|(-2cos(3π((1x)/(2x + 3)) + 1) + 1) + 2|))/(1(3|(-2cos(3π((1x)/(2x + 3)) + 1) + 1) + 2|) + 1)) - 3)) + 5 and g(x) = (2(-5... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(2(1(-4(-2cos(2π(1|x - 1| + 1) + 1) + 1) - 3)^2 + 4(-4(-2cos(2π(1|x - 1| + 1) + 1) + 1) - 3) + 2) + 2) + 1 and g(x) = 2|(-1|(2|(-2(-3|x - 1| + 3)^2 + 3(-3|x - 1| + 3)) - 1| - 3) + 3| - 3) + 1| - 3 from x = 2.0 to x = 2.1. Round to 1 decima... | 6.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3e^(1((-1(5(5(-1(-4x - 3) - 4)^2 + 3(-1(-4x - 3) - 4) + 1)^2 - 5(5(-1(-4x - 3) - 4)^2 + 3(-1(-4x - 3) - 4) + 1) + 2) - 2)/(1(5(5(-1(-4x - 3) - 4)^2 + 3(-1(-4x - 3) - 4) + 1)^2 - 5(5(-1(-4x - 3) - 4)^2 + 3(-1(-4x - 3) - 4) + 1) + 2) + 3))) +... | 13.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5((-1((-2((-3(2|(-1cos(1πx) + 3) - 2| - 1) + 2)/(3(2|(-1cos(1πx) + 3) - 2| - 1) - 1)) + 3)/(2((-3(2|(-1cos(1πx) + 3) - 2| - 1) + 2)/(3(2|(-1cos(1πx) + 3) - 2| - 1) - 1)) + 3)) - 1)/(1((-2((-3(2|(-1cos(1πx) + 3) - 2| - 1) + 2)/(3(2|(-1cos(1πx... | 18.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(3(2|(2(-1e^(1((2x - 1)/(2x + 1))) + 3) - 2) - 3| - 1)) - 3, g(x) = 5((1(5((-1(-3e^(2x) + 1) - 2)/(-2(-3e^(2x) + 1) + 3))^2 + 1((-1(-3e^(2x) + 1) - 2)/(-2(-3e^(2x) + 1) + 3)) + 4) - 2)/(2(5((-1(-3e^(2x) + 1) - 2)/(-2(-3e^(2x) + 1) + 3))^2 ... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3((-1(-3(-1|(1(-3|x| - 2) - 4) + 3| + 2)^2 + 5(-1|(1(-3|x| - 2) - 4) + 3| + 2) - 5) - 1)/(-3(-3(-1|(1(-3|x| - 2) - 4) + 3| + 2)^2 + 5(-1|(1(-3|x| - 2) - 4) + 3| + 2) - 5) + 2))^2 + 3((-1(-3(-1|(1(-3|x| - 2) - 4) + 3| + 2)^2 + 5(-1|(1(-3|x| ... | 1.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -5(-1(-1((1((3(-1|x - 3| - 2) + 3)/(1(-1|x - 3| - 2) + 1)) - 3)/(-1((3(-1|x - 3| - 2) + 3)/(1(-1|x - 3| - 2) + 1)) + 2)) + 5)^2 + 5(-1((1((3(-1|x - 3| - 2) + 3)/(1(-1|x - 3| - 2) + 1)) - 3)/(-1((3(-1|x - 3| - 2) + 3)/(1(-1|x - 3| - 2) + 1)) ... | 195.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|((2(3(-1|(-5(-1x + 4)^2 - 1(-1x + 4) + 5) + 2| - 3) - 2) - 1)/(-2(3(-1|(-5(-1x + 4)^2 - 1(-1x + 4) + 5) + 2| - 3) - 2))) + 1| - 2, g(x) = 5(4(-3(-3sin(2π(5x + 5) - 3)) + 5) - 4) + 2, x = 2.7, and x = 2.8. Round your answer to 1 decimal pla... | 19.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(-1|((-3(-3|((-1((-1x + 3)/(-2x - 3)) - 1)/(-1((-1x + 3)/(-2x - 3)) - 3)) - 3| - 2) - 2)/(3(-3|((-1((-1x + 3)/(-2x - 3)) - 1)/(-1((-1x + 3)/(-2x - 3)) - 3)) - 3| - 2) + 2)) - 1|) + 1)/(-3(-1|((-3(-3|((-1((-1x + 3)/(-2x - 3)) - 1)/(-1((-1x ... | 0.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-2|((-2(-4(2|((2x + 2)/(-3x + 4))| + 1)^2 + 5(2|((2x + 2)/(-3x + 4))| + 1) + 1))/(3(-4(2|((2x + 2)/(-3x + 4))| + 1)^2 + 5(2|((2x + 2)/(-3x + 4))| + 1) + 1) - 2)) - 1| + 1) + 2)/(2(-2|((-2(-4(2|((2x + 2)/(-3x + 4))| + 1)^2 + 5(2|((2x + 2)/... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4((1(-1|((-3(-1(1|x - 1| - 3) - 3))/(-3(-1(1|x - 1| - 3) - 3) - 3)) - 1| + 3))/(-1(-1|((-3(-1(1|x - 1| - 3) - 3))/(-3(-1(1|x - 1| - 3) - 3) - 3)) - 1| + 3) + 2))^2 + 3((1(-1|((-3(-1(1|x - 1| - 3) - 3))/(-3(-1(1|x - 1| - 3) - 3) - 3)) - 1| +... | 34.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2((-1((1(-1|(2|(5x^2 + 4x + 1) - 2| - 1) - 3| + 1))/(-2(-1|(2|(5x^2 + 4x + 1) - 2| - 1) - 3| + 1) + 3)) + 2)/(-3((1(-1|(2|(5x^2 + 4x + 1) - 2| - 1) - 3| + 1))/(-2(-1|(2|(5x^2 + 4x + 1) - 2| - 1) - 3| + 1) + 3)) + 1)) + 1)/(1((-1((1(-1|(2|(5... | 2.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|((1(-1(1((1(2|x - 2| - 2) + 2)/(-2(2|x - 2| - 2) - 1))^2 - 2((1(2|x - 2| - 2) + 2)/(-2(2|x - 2| - 2) - 1)) - 2)^2 + 5(1((1(2|x - 2| - 2) + 2)/(-2(2|x - 2| - 2) - 1))^2 - 2((1(2|x - 2| - 2) + 2)/(-2(2|x - 2| - 2) - 1)) - 2) + 3) + 1)/(-2(-... | 1.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((1(1(2|(5((-1x + 2)/(2x + 1)) + 1)| + 1)^2 + 1(2|(5((-1x + 2)/(2x + 1)) + 1)| + 1) + 2) + 1)/(1(1(2|(5((-1x + 2)/(2x + 1)) + 1)| + 1)^2 + 1(2|(5((-1x + 2)/(2x + 1)) + 1)| + 1) + 2) + 1)) + 2 and g(x) = 3cos(1π(-2|(3|(-5(1x + 4) -... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(2|(3(-1(-5(1x^2 + 1x) + 5) + 3)^2 + 1(-1(-5(1x^2 + 1x) + 5) + 3) - 5) + 3|) + 5 and g(x) = 3|((-1(4(5(-2x^2 + 4) + 1) + 3) - 3)/(-1(4(5(-2x^2 + 4) + 1) + 3) - 1)) + 3| + 2 from x = -1.1 to x = 0.1. Round to 1 decimal place.\n\nPresent the ... | 72.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -5((-1(-3|((1((1(2x + 1) - 3)/(-1(2x + 1) + 2)) - 2)/(-1((1(2x + 1) - 3)/(-1(2x + 1) + 2)) - 3)) + 1| + 3) + 2)/(3(-3|((1((1(2x + 1) - 3)/(-1(2x + 1) + 2)) - 2)/(-1((1(2x + 1) - 3)/(-1(2x + 1) + 2)) - 3)) + 1| + 3) - 2)) + 4 and g(x) = 1sin(... | 0.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2((1(1(-3|(-4((-3x - 1)/(-3x - 1)) - 2) - 1|)^2 - 5(-3|(-4((-3x - 1)/(-3x - 1)) - 2) - 1|) - 1))/(3(1(-3|(-4((-3x - 1)/(-3x - 1)) - 2) - 1|)^2 - 5(-3|(-4((-3x - 1)/(-3x - 1)) - 2) - 1|) - 1) - 2)) + 3, g(x) = 5((-3(-1cos(3π(-3((1x + 3)/(-1x... | 2.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(-3(2|((-2((1((1x + 3)/(3x)) - 3)/(-2((1x + 3)/(3x)) - 3)) - 1)/(-3((1((1x + 3)/(3x)) - 3)/(-2((1x + 3)/(3x)) - 3)) + 1)) + 2| - 3)), g(x) = -1|(1|((-2(3cos(3π(-1x^2 + 4x + 3) - 1) + 2) + 2)/(-3(3cos(3π(-1x^2 + 4x + 3) - 1) + 2))) - 1| - 1)... | 5.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5(-2|((3(2e^(1(1(3x + 3)^2 + 5(3x + 3) + 3)) + 3) - 1)/(-1(2e^(1(1(3x + 3)^2 + 5(3x + 3) + 3)) + 3) + 2)) + 1| + 3)^2 + 5(-2|((3(2e^(1(1(3x + 3)^2 + 5(3x + 3) + 3)) + 3) - 1)/(-1(2e^(1(1(3x + 3)^2 + 5(3x + 3) + 3)) + 3) + 2)) + 1| + 3) + 3 a... | 1.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((-2(1(-1(2(3x - 2) - 1) + 4)) - 3)/(-2(1(-1(2(3x - 2) - 1) + 4)) - 1)) + 2| - 3 and g(x) = -1(3(2(3(4x^2 + 5x - 3) + 4) - 1) + 2) - 4 between the vertical lines x = -1.5 and x = 0.2. Round to 1 decimal place.\n\nPresent the answe... | 58.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1((-2(5(2cos(2π((3(1x - 2) - 3)/(-3(1x - 2) + 4)) + 1))^2 + 5(2cos(2π((3(1x - 2) - 3)/(-3(1x - 2) + 4)) + 1)) - 3) - 1)/(-2(5(2cos(2π((3(1x - 2) - 3)/(-3(1x - 2) + 4)) + 1))^2 + 5(2cos(2π((3(1x - 2) - 3)/(-3(1x - 2) + 4)) + 1)) - 3) - 2)) -... | 112.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-2cos(2π(-1((2(3|(2x^2 - 2x) - 1|) - 3)/(-1(3|(2x^2 - 2x) - 1|) - 1)) - 1) - 2) + 1) + 1 and g(x) = (1((2(-1(-2|(2e^(-1x)) + 3| + 2) + 1) + 3)/(3(-1(-2|(2e^(-1x)) + 3| + 2) + 1) - 1)) + 1)/(-3((2(-1(-2|(2e^(-1x)) + 3| + 2) + 1) +... | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5(-2|((3((2(-4(-5x - 3)^2) + 3)/(3(-4(-5x - 3)^2) + 2)) + 2)/(-2((2(-4(-5x - 3)^2) + 3)/(3(-4(-5x - 3)^2) + 2)) + 1)) - 3| - 3) + 2 and g(x) = 5(1(-2(-2|(-4x^2 - 3x + 1)| - 1)^2 + 4(-2|(-4x^2 - 3x + 1)| - 1)) + 2) + 3 from x = -0.4 to x = -0... | 192.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(3|((3(-1(1(-1x^2 + 2x - 5)^2 - 1(-1x^2 + 2x - 5) + 4) + 5) + 2)/(-2(-1(1(-1x^2 + 2x - 5)^2 - 1(-1x^2 + 2x - 5) + 4) + 5) + 3)) + 1| - 2)^2 + 3(3|((3(-1(1(-1x^2 + 2x - 5)^2 - 1(-1x^2 + 2x - 5) + 4) + 5) + 2)/(-2(-1(1(-1x^2 + 2x - 5)^2 - 1(-... | 19.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(2sin(1π(-1(-1(2(5x^2 - 1x + 2) - 2) + 4) - 2) + 3) + 2)^2 + 3(2sin(1π(-1(-1(2(5x^2 - 1x + 2) - 2) + 4) - 2) + 3) + 2) + 2, g(x) = 5(1(2(-1(1sin(1πx - 2) - 1)^2 + 5(1sin(1πx - 2) - 1) + 5)^2 - 1(-1(1sin(1πx - 2) - 1)^2 + 5(1sin(1πx - 2) - ... | 2.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(1(-3|(-2(2|(-1|x - 2|) - 1|) - 1) - 1| - 1)^2 - 5(-3|(-2(2|(-1|x - 2|) - 1|) - 1) - 1| - 1) + 3) - 2)/(1(1(-3|(-2(2|(-1|x - 2|) - 1|) - 1) - 1| - 1)^2 - 5(-3|(-2(2|(-1|x - 2|) - 1|) - 1) - 1| - 1) + 3)) and g(x) = 2|((1(-5(3|(-2x + 4)| - ... | 0.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-3(2cos(1π(2|(-3|(3|x - 3| + 1) - 1| + 2) - 3|) - 2) - 1)^2 + 5)^2 + 4(-3(2cos(1π(2|(-3|(3|x - 3| + 1) - 1| + 2) - 3|) - 2) - 1)^2 + 5) + 2 and g(x) = 1|(-3sin(2π((-2(-1|((1x + 1)/(-3x - 2)) - 1|))/(-1(-1|((1x + 1)/(-3x - 2)) - 1... | 97.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((1(3|(-3(1|((-1x - 3)/(-2x + 1))| - 2) + 5) + 3|) + 2)/(-2(3|(-3(1|((-1x - 3)/(-2x + 1))| - 2) + 5) + 3|) - 1)) - 3 and g(x) = -5(1sin(3π(-2|((-1(1|x - 1| - 2) - 1)/(-2(1|x - 1| - 2) + 3)) - 3| + 3) - 2) + 2)^2 + 1(1sin(3π(-2|((-... | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|((3(-5(-2|(-3sin(1π(4x - 1) + 1) - 1)| + 2)^2 - 5(-2|(-3sin(1π(4x - 1) + 1) - 1)| + 2) + 1) - 1)/(-1(-5(-2|(-3sin(1π(4x - 1) + 1) - 1)| + 2)^2 - 5(-2|(-3sin(1π(4x - 1) + 1) - 1)| + 2) + 1) + 2)) - 1| - 1 and g(x) = -1|(-3((1(3|((-3x - 3)/(... | 12.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(1|(2(4(1(1|x + 1| + 3) - 3) - 4) + 5)| - 1)^2 - 4(1|(2(4(1(1|x + 1| + 3) - 3) - 4) + 5)| - 1) + 1, g(x) = (-3((-1(1|(-3sin(3π(-2|x + 3| - 1) - 3) - 2)| - 1) + 2)/(-3(1|(-3sin(3π(-2|x + 3| - 1) - 3) - 2)| - 1) - 2)) - 2)/(2((-1(1|(-3sin(3π... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(3|(-2|(-2sin(1π(-3((-3x - 3)/(3x + 1))^2 + 3((-3x - 3)/(3x + 1))) - 2) + 2) - 1|) + 3| + 3) + 1)/(2(3|(-2|(-2sin(1π(-3((-3x - 3)/(3x + 1))^2 + 3((-3x - 3)/(3x + 1))) - 2) + 2) - 1|) + 3| + 3) + 3) and g(x) = 5(-1|(3|(1cos(3π(4x^... | 0.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-4(-2|((1(1sin(2π((3x - 1)/(-2x - 1)) + 3) - 2))/(-2(1sin(2π((3x - 1)/(-2x - 1)) + 3) - 2))) + 1| + 1)^2 + 3(-2|((1(1sin(2π((3x - 1)/(-2x - 1)) + 3) - 2))/(-2(1sin(2π((3x - 1)/(-2x - 1)) + 3) - 2))) + 1| + 1) + 3)^2 - 4(-4(-2|((1... | 84.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(-2e^(1(-2|(-2(-2(-1x + 4) + 4) - 1) - 2| + 1)) + 3) + 2)/(3(-2e^(1(-2|(-2(-2(-1x + 4) + 4) - 1) - 2| + 1)) + 3) + 2) and g(x) = -2(3((-2(2(1e^(-1x) - 1) - 2) + 3)/(3(2(1e^(-1x) - 1) - 2) + 3)) - 4) - 2 from x = -0.7 to x = 1.2. Round to ... | 103.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((1(-1(-2cos(2π(-3|(-2x^2 + 1x - 1) - 3| - 2) + 3))^2 - 5(-2cos(2π(-3|(-2x^2 + 1x - 1) - 3| - 2) + 3)) + 5) + 1)/(-1(-1(-2cos(2π(-3|(-2x^2 + 1x - 1) - 3| - 2) + 3))^2 - 5(-2cos(2π(-3|(-2x^2 + 1x - 1) - 3| - 2) + 3)) + 5) - 2)) + 3... | 0.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3((2(-3cos(2π(-1|((-3((2x + 1)/(2x - 1)) + 1)/(3((2x + 1)/(2x - 1)) + 2))| + 1) + 2) - 3) + 1)/(1(-3cos(2π(-1|((-3((2x + 1)/(2x - 1)) + 1)/(3((2x + 1)/(2x - 1)) + 2))| + 1) + 2) - 3))) + 3 and g(x) = (3(-4((-3(2cos(2π(-3|x| - 2) - 2) + 3) + ... | 2.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(2π(3(2(4(-4(2|x - 1| + 3)^2 - 3(2|x - 1| + 3) - 2) - 3) + 3) - 1)) + 2 and g(x) = -2|(-1|(1e^(1(2(-3|x + 1| - 2) + 1)) - 1) + 2| - 3) + 2| + 3 between the vertical lines x = 1.3 and x = 1.4. Round to 1 decimal place.\n\nPresent... | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((1(-4(-1cos(2π(-2(-2x + 2)^2 + 2(-2x + 2) - 4) - 3) - 2) - 4) - 3)/(2(-4(-1cos(2π(-2(-2x + 2)^2 + 2(-2x + 2) - 4) - 3) - 2) - 4) - 1))^2 + 5((1(-4(-1cos(2π(-2(-2x + 2)^2 + 2(-2x + 2) - 4) - 3) - 2) - 4) - 3)/(2(-4(-1cos(2π(-2(-2x ... | 25.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(-1cos(1π(-1(-1(-5(1|x + 2| - 3)^2 - 2(1|x + 2| - 3) - 4)^2 + 1))) - 1) + 2, g(x) = 2(1|(4((-2(-5x - 2) + 3)/(1(-5x - 2))) + 5) - 1| + 1)^2 - 5(1|(4((-2(-5x - 2) + 3)/(1(-5x - 2))) + 5) - 1| + 1) + 4, x = -1.1, and x = -1.0. Round your answ... | 0.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(2|(4(2(2|(-1|x - 2| + 2) + 1| - 1)^2 - 5(2|(-1|x - 2| + 2) + 1| - 1) - 2)^2 - 2(2(2|(-1|x - 2| + 2) + 1| - 1)^2 - 5(2|(-1|x - 2| + 2) + 1| - 1) - 2) - 1) + 2|) + 3)/(-3(2|(4(2(2|(-1|x - 2| + 2) + 1| - 1)^2 - 5(2|(-1|x - 2| + 2) + 1| - 1) ... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2|(-1|(-1(2|(4x - 4) + 2| - 3)^2 + 1(2|(4x - 4) + 2| - 3) - 2) + 3|) - 2|) - 5 and g(x) = (2(4((-1(-3(-3sin(3πx + 3) - 3) + 4) - 1)/(2(-3(-3sin(3πx + 3) - 3) + 4) + 1)) + 4) + 3)/(-2(4((-1(-3(-3sin(3πx + 3) - 3) + 4) - 1)/(2(-3(-... | 5.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(5(-1(-1|((-2((-2x)/(1x + 1)) - 3)/(2((-2x)/(1x + 1)) + 1)) + 1| + 3)^2 - 4(-1|((-2((-2x)/(1x + 1)) - 3)/(2((-2x)/(1x + 1)) + 1)) + 1| + 3)) - 4) + 1| - 2, g(x) = 4(4(3|(-1(-1|x + 3| - 3)) + 3| + 2) + 1) + 4, x = 0.3, and x = 0.4. Round yo... | -1295.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(-1(1|((3((-3((2x + 1)/(1x + 3)) - 3)/(2((2x + 1)/(1x + 3)) - 1)))/(1((-3((2x + 1)/(1x + 3)) - 3)/(2((2x + 1)/(1x + 3)) - 1)) + 3)) + 2| - 3)) - 2)/(1(-1(1|((3((-3((2x + 1)/(1x + 3)) - 3)/(2((2x + 1)/(1x + 3)) - 1)))/(1((-3((2x + 1)/(1x + ... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(3(-2(1|(-1(-3|x - 3| + 2)^2 - 2(-3|x - 3| + 2)) - 2| + 1) + 4)) + 2)/(2(3(-2(1|(-1(-3|x - 3| + 2)^2 - 2(-3|x - 3| + 2)) - 2| + 1) + 4)) + 3) and g(x) = (-1(-1|(3(-2|(-1cos(3πx) - 1)|)^2 - 1(-2|(-1cos(3πx) - 1)|) - 2) - 2| - 3) - 3)/(-2(-1... | 0.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(-1|(2(-1((2(-1|x - 2| + 2) - 1)/(3(-1|x - 2| + 2) - 2)) + 4) - 3) - 1| + 2) + 2| - 2 and g(x) = -5(1((1(3sin(3π(-1x + 1) - 1) - 3) - 2)/(2(3sin(3π(-1x + 1) - 1) - 3) - 1))^2 + 2)^2 - 3(1((1(3sin(3π(-1x + 1) - 1) - 3) - 2)/(2(3sin(3π(-1x ... | 13.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(1cos(1π((3(3|(-1(-1x^2 + 4) + 2)| - 3) - 2)/(-3(3|(-1(-1x^2 + 4) + 2)| - 3) + 1)) + 2) + 1) - 2| - 2 and g(x) = -1|(2|((1((-2(2x^2 + 1x - 4) - 2)/(3(2x^2 + 1x - 4) - 2)) + 2)/(-2((-2(2x^2 + 1x - 4) - 2)/(3(2x^2 + 1x - 4) - 2)) + 3)) - 2|... | 2.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2(-5((-1(-5(1x^2 + 4x) - 3) + 2)/(-1(-5(1x^2 + 4x) - 3)))^2 + 2((-1(-5(1x^2 + 4x) - 3) + 2)/(-1(-5(1x^2 + 4x) - 3))) + 2) + 3) + 3)/(2(2(-5((-1(-5(1x^2 + 4x) - 3) + 2)/(-1(-5(1x^2 + 4x) - 3)))^2 + 2((-1(-5(1x^2 + 4x) - 3) + 2)/(-... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(-3cos(2π(-5(1(4(-3x - 5) + 2) + 5) + 1) + 3) + 1) + 1, g(x) = (1(-3|(-1(-2(-2|x + 3| - 3)^2 + 4(-2|x + 3| - 3) - 2)^2 - 1(-2(-2|x + 3| - 3)^2 + 4(-2|x + 3| - 3) - 2) + 4)|))/(-2(-3|(-1(-2(-2|x + 3| - 3)^2 + 4(-2|x + 3| - 3) - 2)^2 - 1(-2(... | 1.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(-2|(-5(-3((-3(3cos(1πx + 1) - 2))/(-2(3cos(1πx + 1) - 2) - 2))^2 + 5((-3(3cos(1πx + 1) - 2))/(-2(3cos(1πx + 1) - 2) - 2)) + 3) - 4)| + 1) - 3)/(-1(-2|(-5(-3((-3(3cos(1πx + 1) - 2))/(-2(3cos(1πx + 1) - 2) - 2))^2 + 5((-3(3cos(1πx + 1) - 2)... | 2.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1((2((-1(2(-1(3x + 3) - 5)^2 - 5(-1(3x + 3) - 5) + 4))/(-1(2(-1(3x + 3) - 5)^2 - 5(-1(3x + 3) - 5) + 4))) + 3)/(3((-1(2(-1(3x + 3) - 5)^2 - 5(-1(3x + 3) - 5) + 4))/(-1(2(-1(3x + 3) - 5)^2 - 5(-1(3x + 3) - 5) + 4))) - 2)) - 4, g(x) = -4(-2|(-... | 0.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|((-2(2sin(2π(-1(-5(3x)^2 - 3(3x) - 5)^2 - 3(-5(3x)^2 - 3(3x) - 5)) + 1)) + 2)/(3(2sin(2π(-1(-5(3x)^2 - 3(3x) - 5)^2 - 3(-5(3x)^2 - 3(3x) - 5)) + 1)) + 2)) - 2| + 2 and g(x) = 2sin(2π(2(-1(4((1x)/(-1x + 2)) + 2) + 5)^2 + 5(-1(4((1x)/(-1x +... | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(1cos(3π(2(4((-1((-1x + 1)/(-3x + 4)) - 1)/(3((-1x + 1)/(-3x + 4)) - 2))^2 - 3((-1((-1x + 1)/(-3x + 4)) - 1)/(3((-1x + 1)/(-3x + 4)) - 2)) + 1) + 1) + 1) + 2))/(1(1cos(3π(2(4((-1((-1x + 1)/(-3x + 4)) - 1)/(3((-1x + 1)/(-3x + 4)) -... | 7.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-5(-2sin(1π(-1(2(-4x^2 - 1x) - 1)) + 3) - 2) + 5)^2 + 2(-5(-2sin(1π(-1(2(-4x^2 - 1x) - 1)) + 3) - 2) + 5) + 5 and g(x) = -3(-1(-1|(3|(-3|x - 1| + 2) - 1| - 2) + 3| - 2)^2 - 3(-1|(3|(-3|x - 1| + 2) - 1| - 2) + 3| - 2) - 4)^2 - 1(-... | 84.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4(4(-1(3(-2e^(-2(1|x + 1| - 3)) + 3) - 5)^2 + 2)) + 4, g(x) = 1e^(2(-5(1(5(-3|x + 2| + 3)^2 - 2(-3|x + 2| + 3) - 3) + 1) - 4)) - 3, x = -4.4, and x = -4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 10.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3((3(-3|((1((-3(-3e^(-2x)) + 2)/(2(-3e^(-2x)) - 1)) + 3)/(-3((-3(-3e^(-2x)) + 2)/(2(-3e^(-2x)) - 1)) + 4)) - 1|) - 3)/(-1(-3|((1((-3(-3e^(-2x)) + 2)/(2(-3e^(-2x)) - 1)) + 3)/(-3((-3(-3e^(-2x)) + 2)/(2(-3e^(-2x)) - 1)) + 4)) - 1|) + 2)) + 1... | 14.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(-5(-5(3cos(3π((2((3x - 3)/(-2x + 3)))/(-3((3x - 3)/(-2x + 3)) + 4)) + 1) + 3) + 2)^2 - 2(-5(3cos(3π((2((3x - 3)/(-2x + 3)))/(-3((3x - 3)/(-2x + 3)) + 4)) + 1) + 3) + 2) + 2) + 3)/(-3(-5(-5(3cos(3π((2((3x - 3)/(-2x + 3)))/(-3((3x - 3)/(-2x... | 2.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3((2(-1(3e^(-2((-2(2x - 2) - 3)/(1(2x - 2) + 2)))) - 5))/(-2(-1(3e^(-2((-2(2x - 2) - 3)/(1(2x - 2) + 2)))) - 5) - 1)))/(1((2(-1(3e^(-2((-2(2x - 2) - 3)/(1(2x - 2) + 2)))) - 5))/(-2(-1(3e^(-2((-2(2x - 2) - 3)/(1(2x - 2) + 2)))) - 5) - 1))),... | 1.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(1(-1|((2(-3(-2|x + 3| - 3)^2 - 4(-2|x + 3| - 3) - 5) - 2)/(2(-3(-2|x + 3| - 3)^2 - 4(-2|x + 3| - 3) - 5) + 3))| + 2)^2 - 2(-1|((2(-3(-2|x + 3| - 3)^2 - 4(-2|x + 3| - 3) - 5) - 2)/(2(-3(-2|x + 3| - 3)^2 - 4(-2|x + 3| - 3) - 5) + 3))| + 2) ... | 222.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1((1(4(-2(-5(1x^2 - 3x) - 3)^2 - 5(-5(1x^2 - 3x) - 3) + 3) + 5) + 3)/(2(4(-2(-5(1x^2 - 3x) - 3)^2 - 5(-5(1x^2 - 3x) - 3) + 3) + 5))) + 1, g(x) = -5(2|(-3cos(1π(1|(-1|x - 1|) + 1| - 2) + 3) - 3) + 1|)^2 - 2(2|(-3cos(1π(1|(-1|x - 1|) + 1| - 2... | 7.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(-3(-4((2((-3(-3x - 4) + 1)/(-2(-3x - 4) + 3)) - 3)/(1((-3(-3x - 4) + 1)/(-2(-3x - 4) + 3)) - 3)) + 5)^2 + 5(-4((2((-3(-3x - 4) + 1)/(-2(-3x - 4) + 3)) - 3)/(1((-3(-3x - 4) + 1)/(-2(-3x - 4) + 3)) - 3)) + 5) + 5) + 5 and g(x) = -2sin(1π(1(... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((-2(-3((-3((1(3cos(2πx + 1) - 3) + 3)/(-1(3cos(2πx + 1) - 3) - 2)) - 3)/(1((1(3cos(2πx + 1) - 3) + 3)/(-1(3cos(2πx + 1) - 3) - 2))))^2 + 3((-3((1(3cos(2πx + 1) - 3) + 3)/(-1(3cos(2πx + 1) - 3) - 2)) - 3)/(1((1(3cos(2πx + 1) - 3) ... | 1.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(3|(-2|((-1(5(1x^2 + 3)^2 + 4) - 2)/(-3(5(1x^2 + 3)^2 + 4) + 1))| + 1) + 2| - 3) + 1 and g(x) = -1((-2(-1((2(-2e^(1x)) + 1)/(2(-2e^(1x))))^2 + 3) - 2)/(3(-1((2(-2e^(1x)) + 1)/(2(-2e^(1x))))^2 + 3) + 3))^2 - 4((-2(-1((2(-2e^(1x)) + 1)/(2(-2... | 66.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(1(2e^(1((-2(-3(-3x^2 + 1x + 2) - 2) + 1)/(1(-3(-3x^2 + 1x + 2) - 2) - 3))) + 3) - 4) + 3)/(-3(1(2e^(1((-2(-3(-3x^2 + 1x + 2) - 2) + 1)/(1(-3(-3x^2 + 1x + 2) - 2) - 3))) + 3) - 4) - 3) and g(x) = 1sin(1π(1(-3(-3|(1x + 3) + 1| - 1... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|(-1(5(-1|((-1(4x + 5))/(2(4x + 5) - 3)) + 1| + 3) - 2) + 2) - 3| - 1, g(x) = 4(-1(-3e^(2(-3(-2x^2 + 2x + 2)^2 + 4(-2x^2 + 2x + 2) + 5)) + 2)^2 + 5(-3e^(2(-3(-2x^2 + 2x + 2)^2 + 4(-2x^2 + 2x + 2) + 5)) + 2) + 3) + 1, x = 0.1, and x = 0.9. ... | 39.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2((-1((-2(-1(2(-1x^2 + 3x - 5)^2 + 3(-1x^2 + 3x - 5) - 5) + 3) - 2)/(2(-1(2(-1x^2 + 3x - 5)^2 + 3(-1x^2 + 3x - 5) - 5) + 3) + 1)))/(1((-2(-1(2(-1x^2 + 3x - 5)^2 + 3(-1x^2 + 3x - 5) - 5) + 3) - 2)/(2(-1(2(-1x^2 + 3x - 5)^2 + 3(-1x^2 + 3x - ... | 36.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((1(1|(-2|(1(5x + 2) - 5) - 2| + 3) + 1| - 3) + 1)/(-1(1|(-2|(1(5x + 2) - 5) - 2| + 3) + 1| - 3) + 2)) + 2 and g(x) = (3(1|(1((-1((-2x - 1)/(-1x - 2)))/(3((-2x - 1)/(-1x - 2)) + 2)) + 2) - 1| - 2) - 1)/(-3(1|(1((-1((-2x - 1)/(-1x -... | 25.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(-2(-3|(1|(-2((3x + 2)/(1x)) - 4) + 1| - 3) + 1| - 2)^2 - 4(-3|(1|(-2((3x + 2)/(1x)) - 4) + 1| - 3) + 1| - 2) + 5) - 2)/(2(-2(-3|(1|(-2((3x + 2)/(1x)) - 4) + 1| - 3) + 1| - 2)^2 - 4(-3|(1|(-2((3x + 2)/(1x)) - 4) + 1| - 3) + 1| - 2) + 5) - ... | 1.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2((-2(-4((1((2((-1x + 3)/(2x - 1)) + 2)/(-1((-1x + 3)/(2x - 1)) - 2)) + 3)/(-3((2((-1x + 3)/(2x - 1)) + 2)/(-1((-1x + 3)/(2x - 1)) - 2)) - 1)) + 3))/(-2(-4((1((2((-1x + 3)/(2x - 1)) + 2)/(-1((-1x + 3)/(2x - 1)) - 2)) + 3)/(-3((2((-1x + 3)/(... | 0.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|(1((2(-1|(-3cos(3π(-4x^2 - 1x) + 2) - 2) + 3|) + 3)/(-3(-1|(-3cos(3π(-4x^2 - 1x) + 2) - 2) + 3|) - 3))^2) + 2| + 3, g(x) = (-2(1(5(1(1x^2 - 3x - 4) + 3)^2 - 2(1(1x^2 - 3x - 4) + 3) - 2) + 1) + 1)/(3(1(5(1(1x^2 - 3x - 4) + 3)^2 - 2(1(1x^2 -... | 6.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(3(-1|(-4((-1(3|x - 2| - 3) - 2)/(-3(3|x - 2| - 3)))) - 2|)^2 - 3) + 2)/(2(3(-1|(-4((-1(3|x - 2| - 3) - 2)/(-3(3|x - 2| - 3)))) - 2|)^2 - 3) + 1) and g(x) = 3(5(-4(4(3x^2 + 1x - 5)^2 + 5(3x^2 + 1x - 5) - 2) + 5)^2 + 1(-4(4(3x^2 +... | 196.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(3|(-2cos(3π(-2|((1(1x - 5) - 3)/(2(1x - 5) - 1)) + 2| + 3) + 1) + 1)|) - 2)/(3(3|(-2cos(3π(-2|((1(1x - 5) - 3)/(2(1x - 5) - 1)) + 2| + 3) + 1) + 1)|)) and g(x) = (-1(-5(-3cos(3π(3(-5x^2 + 1x - 5) + 4) + 3)) - 5) - 2)/(-2(-5(-3co... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(-4((-1(-2|(-1|((-1x + 1)/(1x - 3)) - 3| - 2) - 2| - 2) + 1)/(1(-2|(-1|((-1x + 1)/(1x - 3)) - 3| - 2) - 2| - 2))) - 4) + 1| - 2 and g(x) = -4(4((-3(1|(-5x^2 + 5x + 2) + 3| - 2))/(-3(1|(-5x^2 + 5x + 2) + 3| - 2) - 3))^2 - 3((-3(1|(-5x^2 + 5... | 5.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-1|(-3|(-1|(-4(2sin(3πx + 2) - 1) + 1)| + 3)| + 1) + 2| - 2)^2 + 3(-1|(-3|(-1|(-4(2sin(3πx + 2) - 1) + 1)| + 3)| + 1) + 2| - 2) - 2 and g(x) = -1|(-4(-3((2(1sin(3πx + 2) - 1) - 3)/(1(1sin(3πx + 2) - 1) - 3))^2 - 5((2(1sin(3πx + 2... | 412.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(2|(2|(-3|(5(-1|x| - 1) + 2) - 1| + 1) - 3| - 1) + 1| - 3) - 2| + 2 and g(x) = 1(-3|(2(1(4x - 2)^2 - 5(4x - 2) + 5)^2 + 1(1(4x - 2)^2 - 5(4x - 2) + 5)) - 1| - 1)^2 - 3(-3|(2(1(4x - 2)^2 - 5(4x - 2) + 5)^2 + 1(1(4x - 2)^2 - 5(4x - ... | 84.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(1π(-1((3(-1(4((-1x + 3)/(2x + 3))^2 + 5((-1x + 3)/(2x + 3)) + 2) + 3) + 2)/(1(-1(4((-1x + 3)/(2x + 3))^2 + 5((-1x + 3)/(2x + 3)) + 2) + 3) - 2)) - 5)) and g(x) = (1(2(-3|((-3(-2|x + 1| + 1) + 1)/(-2(-2|x + 1| + 1) + 3))| + 2) -... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(-5(4(-1((2(-2cos(3πx - 2) - 1) + 3)/(-3(-2cos(3πx - 2) - 1) - 2))^2 - 5((2(-2cos(3πx - 2) - 1) + 3)/(-3(-2cos(3πx - 2) - 1) - 2)) - 4) - 2) + 1))/(2(-5(4(-1((2(-2cos(3πx - 2) - 1) + 3)/(-3(-2cos(3πx - 2) - 1) - 2))^2 - 5((2(-2cos(3πx - 2... | 13.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2((-1((1(2|(-1(-5x + 4)^2 + 3(-5x + 4) - 5) - 3| - 2))/(2(2|(-1(-5x + 4)^2 + 3(-5x + 4) - 5) - 3| - 2) - 1)) + 1)/(-1((1(2|(-1(-5x + 4)^2 + 3(-5x + 4) - 5) - 3| - 2))/(2(2|(-1(-5x + 4)^2 + 3(-5x + 4) - 5) - 3| - 2) - 1)) - 2))^2 + 4((-1((1(... | 1.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|((3(-3|(-2|(-1|(-1sin(3πx - 2) - 1) - 3| + 1) + 3| - 3) - 3| + 1) - 3)/(1(-3|(-2|(-1|(-1sin(3πx - 2) - 1) - 3| + 1) + 3| - 3) - 3| + 1) + 1)) - 1| and g(x) = -2((2((-3(3(-1sin(1πx + 1) - 1) + 5) - 3)/(-3(3(-1sin(1πx + 1) - 1) + 5) - 1)))/(... | 39.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((2(3|((-1(1(1x^2 - 3x - 1) - 1) - 3)/(-2(1(1x^2 - 3x - 1) - 1) - 3)) + 2| - 1) - 1)/(3(3|((-1(1(1x^2 - 3x - 1) - 1) - 3)/(-2(1(1x^2 - 3x - 1) - 1) - 3)) + 2| - 1))) - 2| + 2 and g(x) = 1(1(-1sin(1π((3(3|x - 3| - 3))/(-2(3|x - 3| ... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3cos(1π(-3|(2|(-1(-3|(1|x - 3| - 1)| - 2)^2 - 4(-3|(1|x - 3| - 1)| - 2) - 1) - 3| + 2) - 2| - 2) - 2) - 1 and g(x) = -2|(-1|(2cos(1π(1((1x - 3)/(1x)) - 1) + 1) + 2) + 1| - 3) + 2| + 2 from x = -4.0 to x = -3.9. Round to 1 decimal place.\n\n... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-2sin(2π(-1|(-2|(4(2|x - 2| + 3) + 2) + 1| + 3) + 1| - 1) - 1) - 1)^2 + 1(-2sin(2π(-1|(-2|(4(2|x - 2| + 3) + 2) + 1| + 3) + 1| - 1) - 1) - 1) + 5 and g(x) = (1((3(3(-1e^(-1(4x + 3)) - 2)^2 + 5(-1e^(-1(4x + 3)) - 2) - 4) + 1)/(-2(... | 0.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(1|(-3|(-4(2|(2|x - 1|)| - 2)^2 - 2(2|(2|x - 1|)| - 2) + 3) - 3| - 1) + 1| - 3) - 1 and g(x) = (-3(-5((3((-1(-2|x + 1| + 1) - 1)/(-3(-2|x + 1| + 1) - 2)) + 3)/(3((-1(-2|x + 1| + 1) - 1)/(-3(-2|x + 1| + 1) - 2)) - 2))^2 + 4) - 1)/(-1(-5((3((... | 3.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(1sin(3π(-4(-2|(2(1x + 5)^2 + 5(1x + 5)) - 3| - 3) - 3)) - 2)^2 - 2(1sin(3π(-4(-2|(2(1x + 5)^2 + 5(1x + 5)) - 3| - 3) - 3)) - 2) - 4, g(x) = 2|((-1(-3cos(2π(1(-3|x - 1| + 1)^2 - 3(-3|x - 1| + 1) - 2) + 2) + 3) + 3)/(1(-3cos(2π(1(-3|x - 1| +... | 259.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1(-1sin(1π(2|(2(2|x + 1| + 2)^2 - 1(2|x + 1| + 2) - 2) + 2| - 1) - 3) - 3)^2 - 4) - 3)/(3(1(-1sin(1π(2|(2(2|x + 1| + 2)^2 - 1(2|x + 1| + 2) - 2) + 2| - 1) - 3) - 3)^2 - 4) - 2) and g(x) = -5(4((-1(-3|((2x - 1)/(-3x - 2)) + 2| - 1... | 12.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(-1(-4(1(3(-3|x - 2| - 1) + 1) + 2)^2 + 3(1(3(-3|x - 2| - 1) + 1) + 2) + 1) - 1) + 1 and g(x) = -2(-5(-3cos(3π((-2(1|x - 1|) - 3)/(3(1|x - 1|) - 2)))) - 2) - 3 from x = 1.9 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaT... | 1.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(-1(3|(5((-3(3|x| - 1) + 3)/(-2(3|x| - 1) + 1))^2 + 5((-3(3|x| - 1) + 3)/(-2(3|x| - 1) + 1)) + 2) + 2| - 1) - 1), g(x) = 3|(-1(4(1|(-1cos(2πx + 3) - 1)| - 1)^2 - 2(1|(-1cos(2πx + 3) - 1)| - 1) - 5)^2 + 1(4(1|(-1cos(2πx + 3) - 1)| - 1)^2 - ... | 274.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(-1((-1(-1sin(1π(-2((-3x)/(1x - 2)) + 2) - 2) + 1) - 1)/(-3(-1sin(1π(-2((-3x)/(1x - 2)) + 2) - 2) + 1) + 2)) + 3) - 3, g(x) = 2|(3(-3(-3|(-2|x + 3| + 1)| - 2) - 5) + 5)| - 3, x = -2.9, and x = -1.7. Round your answer to 1 decimal place.\n\... | 68.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1(5((2((2(3x^2 + 5x + 3) + 2)/(-1(3x^2 + 5x + 3) + 2)) + 3)/(1((2(3x^2 + 5x + 3) + 2)/(-1(3x^2 + 5x + 3) + 2)))) + 3) + 4)^2 - 1(-1(5((2((2(3x^2 + 5x + 3) + 2)/(-1(3x^2 + 5x + 3) + 2)) + 3)/(1((2(3x^2 + 5x + 3) + 2)/(-1(3x^2 + 5... | 92.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(-4((1(1(2|(3e^(-1x) - 3) + 2| - 1)^2 + 1(2|(3e^(-1x) - 3) + 2| - 1) - 2) - 3)/(-2(1(2|(3e^(-1x) - 3) + 2| - 1)^2 + 1(2|(3e^(-1x) - 3) + 2| - 1) - 2) - 2)) - 1) - 5 and g(x) = -1|(-3|(1|(-3sin(1π(-2x^2 - 5x - 4) + 3) + 3) + 1| + 2)| - 1) -... | 0.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(2π((-2(5(-2(5(5x^2 + 4x)^2 - 3(5x^2 + 4x) - 5) + 3) + 2) - 3)/(-2(5(-2(5(5x^2 + 4x)^2 - 3(5x^2 + 4x) - 5) + 3) + 2) - 3)) + 2) - 3 and g(x) = -2|(1(-5(-3(-2e^(1x)) - 3)^2 - 4(-3(-2e^(1x)) - 3) + 1) + 1) - 2| + 3 between the ver... | 1.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(1e^(1(-2|(-1((-2((2x - 2)/(-1x - 1)) + 2)/(1((2x - 2)/(-1x - 1)) - 3)) - 5) + 3| + 2)) - 3) - 1)/(-2(1e^(1(-2|(-1((-2((2x - 2)/(-1x - 1)) + 2)/(1((2x - 2)/(-1x - 1)) - 3)) - 5) + 3| + 2)) - 3) - 3) and g(x) = 5(-3|(2cos(1π(-1(-5x^2 + 2x -... | 2.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(-2(2sin(2π(3((-3(-4x^2 - 5x + 4))/(-2(-4x^2 - 5x + 4) + 3))^2 - 3((-3(-4x^2 - 5x + 4))/(-2(-4x^2 - 5x + 4) + 3)) - 2) + 2) + 2)^2 - 3(2sin(2π(3((-3(-4x^2 - 5x + 4))/(-2(-4x^2 - 5x + 4) + 3))^2 - 3((-3(-4x^2 - 5x + 4))/(-2(-4x^2 - 5x + 4)... | 3.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(-2sin(1π((2(1(1|(-1|x - 1| - 2) - 2| + 3) + 2) - 3)/(-1(1(1|(-1|x - 1| - 2) - 2| + 3) + 2) + 3)) + 3) + 2))/(2(-2sin(1π((2(1(1|(-1|x - 1| - 2) - 2| + 3) + 2) - 3)/(-1(1(1|(-1|x - 1| - 2) - 2| + 3) + 2) + 3)) + 3) + 2) - 1) and g(x) = (3(... | 0.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(3(3|(-2sin(1π(-2|(-4x - 1)| - 1) - 2) + 1)| - 3)^2 - 4(3|(-2sin(1π(-2|(-4x - 1)| - 1) - 2) + 1)| - 3) - 2)^2 - 3(3(3|(-2sin(1π(-2|(-4x - 1)| - 1) - 2) + 1)| - 3)^2 - 4(3|(-2sin(1π(-2|(-4x - 1)| - 1) - 2) + 1)| - 3) - 2) - 3, g(x) = 2sin(3π... | 28.3 | MATH |
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