messages listlengths 1 1 | ground_truth stringlengths 3 8 | dataset stringclasses 1
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[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3((-2(-1sin(3π((-2(-1x + 2) - 1)/(2(-1x + 2) - 3)) - 2) - 2) - 1)/(-2(-1sin(3π((-2(-1x + 2) - 1)/(2(-1x + 2) - 3)) - 2) - 2) + 3)) + 3)/(2((-2(-1sin(3π((-2(-1x + 2) - 1)/(2(-1x + 2) - 3)) - 2) - 2) - 1)/(-2(-1sin(3π((-2(-1x + 2) - 1)/(2(-1... | 2.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(-3(-2((2((1x + 1)/(1x)) + 3)/(-3((1x + 1)/(1x)))) - 1)^2 - 4(-2((2((1x + 1)/(1x)) + 3)/(-3((1x + 1)/(1x)))) - 1) - 3) - 1)/(-1(-3(-2((2((1x + 1)/(1x)) + 3)/(-3((1x + 1)/(1x)))) - 1)^2 - 4(-2((2((1x + 1)/(1x)) + 3)/(-3((1x + 1)/(1x)))) - ... | 4.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(-1(2((2(-5x + 3) + 2)/(2(-5x + 3) - 3)) + 3) - 3) - 3)/(-1(-1(2((2(-5x + 3) + 2)/(2(-5x + 3) - 3)) + 3) - 3) + 2), g(x) = -1((2(5((-1x - 2)/(-2x - 1)) - 1) - 2)/(2(5((-1x - 2)/(-2x - 1)) - 1) - 1)) + 5, x = -3.5, and x = 0.4. Round your ... | 7.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(-1((-2(-2sin(2π(-5x - 5) + 3) + 2) + 2)/(-2(-2sin(2π(-5x - 5) + 3) + 2) - 3))^2 - 3((-2(-2sin(2π(-5x - 5) + 3) + 2) + 2)/(-2(-2sin(2π(-5x - 5) + 3) + 2) - 3)))^2 + 5(-1((-2(-2sin(2π(-5x - 5) + 3) + 2) + 2)/(-2(-2sin(2π(-5x - 5) + 3) + 2) -... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3π(3((-2(-1|(2|x - 3|) + 3| + 3) - 3)/(1(-1|(2|x - 3|) + 3| + 3) - 2))^2 - 1((-2(-1|(2|x - 3|) + 3| + 3) - 3)/(1(-1|(2|x - 3|) + 3| + 3) - 2)) - 4) - 1) - 2 and g(x) = 1e^(1((-1((1((-2x)/(2x - 3)) + 3)/(-1((-2x)/(2x - 3)) + 2))... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(-2|(-2e^(1(-4((-2x)/(2x - 1))^2 + 4((-2x)/(2x - 1)) - 3)) + 2)| - 1)^2 + 3(-2|(-2e^(1(-4((-2x)/(2x - 1))^2 + 4((-2x)/(2x - 1)) - 3)) + 2)| - 1) + 3 and g(x) = 1|(-1(2|(5x - 2) - 2| + 1)^2 - 2(2|(5x - 2) - 2| + 1) - 4) + 3| + 2 from x = 0.2... | 70.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(1|(-1e^(-1(1((-2x - 1)/(-2x - 3))^2 - 5((-2x - 1)/(-2x - 3)) - 3)) - 2) + 2|)| - 1 and g(x) = (-1((1(4(1sin(3πx + 3) + 1)^2 + 4) - 1)/(2(4(1sin(3πx + 3) + 1)^2 + 4) - 1)) - 1)/(3((1(4(1sin(3πx + 3) + 1)^2 + 4) - 1)/(2(4(1sin(3πx... | 2.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((-3(-3(4(4x - 2)^2 - 5(4x - 2) - 5)) - 2)/(3(-3(4(4x - 2)^2 - 5(4x - 2) - 5)) - 2)) + 2 and g(x) = 3(3|(-1|(-2x^2 + 4) - 2| + 2)| - 3)^2 + 1(3|(-1|(-2x^2 + 4) - 2| + 2)| - 3) - 4 between the vertical lines x = 1.1 and x = 1.3. Ro... | 1.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(1|(-4(2|(-2sin(2πx + 2) - 1) + 2| - 3)^2 - 2(2|(-2sin(2πx + 2) - 1) + 2| - 3) + 3) + 1| - 3) - 1 and g(x) = -2(-1sin(1π(-1(-5x^2 - 2x - 2) + 2) - 1))^2 + 5(-1sin(1π(-1(-5x^2 - 2x - 2) + 2) - 1)) - 4 from x = -5.0 to x = -4.8. Round to 1 d... | 2.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-3|((-2(-3(-2x - 1) - 5) + 1)/(-1(-3(-2x - 1) - 5))) - 3| + 1) - 4 and g(x) = 3|(3|(-1(-1x - 5) + 2) - 2|) + 1| + 2 between the vertical lines x = 0.3 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: ... | 108.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|((3((2(-1|(2|x + 3| + 1) - 2| - 3) + 1)/(3(-1|(2|x + 3| + 1) - 2| - 3) + 3)) + 3)/(-1((2(-1|(2|x + 3| + 1) - 2| - 3) + 1)/(3(-1|(2|x + 3| + 1) - 2| - 3) + 3)))) + 2| and g(x) = -3(-2((2(-2x - 3) + 1)/(3(-2x - 3) - 2))^2 - 2((2(-2x - 3) + ... | 8.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(-1|(-1(1|(-2|x - 1| + 3) + 3|) + 5) - 3| + 1)^2 + 1(-1|(-1(1|(-2|x - 1| + 3) + 3|) + 5) - 3| + 1) + 4 and g(x) = 1|(-1|(3|((-2x + 1)/(-3x + 1)) - 1|) - 2| + 2) - 1| - 1 from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answ... | 13.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(-3(-3sin(1π(-1|(-3|x|) - 1| + 1) + 3) + 1)^2 - 1(-3sin(1π(-1|(-3|x|) - 1| + 1) + 3) + 1) + 3) - 1)/(-1(-3(-3sin(1π(-1|(-3|x|) - 1| + 1) + 3) + 1)^2 - 1(-3sin(1π(-1|(-3|x|) - 1| + 1) + 3) + 1) + 3) + 2) and g(x) = -2sin(3π(3(1(5x - 5)^2 - ... | 2.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-1cos(1π((3(2(2x^2 - 1x - 1) - 2) - 1)/(2(2(2x^2 - 1x - 1) - 2) - 1)) - 1)) - 1 and g(x) = -3cos(2π(4(-2|(4x + 2) + 1| - 1) - 2) - 2) between the vertical lines x = 3.2 and x = 3.3000000000000003. Round to 1 decimal place.\n\nPres... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(3sin(3π(2|(3|(1x - 4) - 3| - 3) + 2| - 2) + 1) + 1)^2 + 1(3sin(3π(2|(3|(1x - 4) - 3| - 3) + 2| - 2) + 1) + 1) - 5 and g(x) = -2|(-1(2(-1x^2 + 2x + 3)^2 - 2(-1x^2 + 2x + 3) - 5)^2 + 3(2(-1x^2 + 2x + 3)^2 - 2(-1x^2 + 2x + 3) - 5) + 1) + 1| ... | 1.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(3(3|(2|(3sin(3πx - 2) - 1) + 2|) - 3| + 3)^2 - 5(3|(2|(3sin(3πx - 2) - 1) + 2|) - 3| + 3) - 4) - 1| + 3 and g(x) = 2|(2(1(-2cos(2πx - 1) + 3)^2 + 2(-2cos(2πx - 1) + 3) - 4) + 2)| - 2 from x = 4.6 to x = 4.699999999999999. Round to 1 decim... | 7.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3e^(-1((2((2(2|(-4x + 2) - 1|) + 1)/(1(2|(-4x + 2) - 1|) + 2)) + 3)/(2((2(2|(-4x + 2) - 1|) + 1)/(1(2|(-4x + 2) - 1|) + 2)) + 3))) - 1 and g(x) = -1|(-1e^(-1(3(-5x^2 + 4) - 1)) + 3) - 3| - 2 from x = -0.8 to x = 0.8. Round to 1 decimal plac... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(1|(-2|(1(-4x - 4) - 1)| + 2) + 3| + 2) - 3| + 1 and g(x) = (-2(-3cos(2π((1(-3|x - 3| - 2) + 1)/(2(-3|x - 3| - 2))) - 2) - 1) + 1)/(-3(-3cos(2π((1(-3|x - 3| - 2) + 1)/(2(-3|x - 3| - 2))) - 2) - 1)) from x = -0.5 to x = -0.4. Round to 1 de... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(-4(-5(2|(-3sin(2πx - 3) - 2) + 3| + 1) + 4)^2 - 2) + 5, g(x) = -4(-5(-1|(1x^2 - 3x) - 3| - 2) - 1) + 5, x = -2.1, and x = -2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 67.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|((-3((2(-3|(-2|x + 3|) + 2| + 1) + 2)/(2(-3|(-2|x + 3|) + 2| + 1) - 1)) - 2)/(3((2(-3|(-2|x + 3|) + 2| + 1) + 2)/(2(-3|(-2|x + 3|) + 2| + 1) - 1)) - 2)) - 1| - 1 and g(x) = 2((1(-2cos(1π((-3x + 1)/(-1x - 2)) - 1)) - 3)/(-3(-2cos(1π((-3x +... | 1.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(5(1cos(1π((1((-1x - 3)/(-3x)) + 2)/(2((-1x - 3)/(-3x)) + 3))) + 1) - 3)^2 - 2 and g(x) = 1(4(-3((-1x)/(-3x + 1))^2 - 4((-1x)/(-3x + 1)) - 2) + 3) from x = -0.6 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: ... | 3.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-1(-1cos(2π(4((2x - 3)/(1x))^2 + 4((2x - 3)/(1x)) + 4) + 1) + 2) + 1) + 2| + 2 and g(x) = -2sin(3π((-3(-3(-1x^2 + 5x - 5) + 3) + 2)/(1(-3(-1x^2 + 5x - 5) + 3) - 2)) - 2) + 1 between the vertical lines x = 0.4 and x = 0.5. Round t... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-2((-3((3(-1x^2 - 1x + 5))/(-3(-1x^2 - 1x + 5) - 3)))/(1((3(-1x^2 - 1x + 5))/(-3(-1x^2 - 1x + 5) - 3)) - 2))^2 - 5((-3((3(-1x^2 - 1x + 5))/(-3(-1x^2 - 1x + 5) - 3)))/(1((3(-1x^2 - 1x + 5))/(-3(-1x^2 - 1x + 5) - 3)) - 2)) - 1) - 3... | 2.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(5((-1(1|(-3|x|) + 2| - 2) + 3)/(-3(1|(-3|x|) + 2| - 2) + 2)) - 3) + 5 and g(x) = 4(-2cos(1π(2|(1x^2 + 1x) - 3|) - 1) - 3)^2 + 2(-2cos(1π(2|(1x^2 + 1x) - 3|) - 1) - 3) + 1 from x = 1.2 to x = 1.4. Round to 1 decimal place.\n\nPresent the an... | 12.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(-3sin(2π(1((2(-1x + 4) + 3)/(-1(-1x + 4) - 2))^2 + 4((2(-1x + 4) + 3)/(-1(-1x + 4) - 2)) - 3) + 2) + 2) - 1, g(x) = -3sin(3π(2((1(-2x + 3) - 3)/(1(-2x + 3) - 2)) - 2)) - 2, x = 0.6, and x = 0.7. Round your answer to 1 decimal place.\n\nPr... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-5(5((-2(-5x^2 - 2x + 2) - 3)/(2(-5x^2 - 2x + 2) + 2))^2 + 3((-2(-5x^2 - 2x + 2) - 3)/(2(-5x^2 - 2x + 2) + 2)) + 1) - 5) + 2| - 3 and g(x) = -3|(2(-3sin(1π(-4x^2 - 4x - 1) - 2) - 1)^2 - 4(-3sin(1π(-4x^2 - 4x - 1) - 2) - 1) - 2) ... | 3.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(2sin(3π((-2(-1(3x^2 + 2)^2 + 1(3x^2 + 2) + 5))/(3(-1(3x^2 + 2)^2 + 1(3x^2 + 2) + 5))) - 1) - 3) + 4 and g(x) = (-2(1(-3sin(3π(-4x) - 3) + 3)^2 - 1(-3sin(3π(-4x) - 3) + 3) - 3) - 3)/(-2(1(-3sin(3π(-4x) - 3) + 3)^2 - 1(-3sin(3π(-4x) - 3) + 3... | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5((-1(1((3(-2|x - 1| + 1) - 1)/(-3(-2|x - 1| + 1))) + 1) - 2)/(-3(1((3(-2|x - 1| + 1) - 1)/(-3(-2|x - 1| + 1))) + 1)))^2 + 1((-1(1((3(-2|x - 1| + 1) - 1)/(-3(-2|x - 1| + 1))) + 1) - 2)/(-3(1((3(-2|x - 1| + 1) - 1)/(-3(-2|x - 1| + 1))) + 1)))... | 2.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(1(-3sin(2π(3(-3x^2 + 1x + 4) - 5) - 2) + 2) - 1)^2 - 4(1(-3sin(2π(3(-3x^2 + 1x + 4) - 5) - 2) + 2) - 1) - 5 and g(x) = (-1(2(1((-2x - 2)/(3x - 2)) - 2) - 5) + 2)/(-3(2(1((-2x - 2)/(3x - 2)) - 2) - 5) - 3) between the vertical line... | 0.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|((-1(3|(-5(-3e^(1x) + 2) + 3) - 1|) + 3)/(-3(3|(-5(-3e^(1x) + 2) + 3) - 1|)))| - 1 and g(x) = (-2(-3(2|(3x^2 - 5x + 5) + 3| + 1)^2 + 4(2|(3x^2 - 5x + 5) + 3| + 1) - 5) - 2)/(3(-3(2|(3x^2 - 5x + 5) + 3| + 1)^2 + 4(2|(3x^2 - 5x + 5) + 3| + 1... | 4.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2(3(1(2e^(1x) - 2)^2 - 3(2e^(1x) - 2) - 5)^2 - 1(1(2e^(1x) - 2)^2 - 3(2e^(1x) - 2) - 5) + 1)^2 - 3(3(1(2e^(1x) - 2)^2 - 3(2e^(1x) - 2) - 5)^2 - 1(1(2e^(1x) - 2)^2 - 3(2e^(1x) - 2) - 5) + 1) + 5) + 3)/(-2(2(3(1(2e^(1x) - 2)^2 - 3(... | 2.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|((-3(-2|(1|(-2cos(3πx) - 2) - 3| - 1) - 2| - 3) + 3)/(-2(-2|(1|(-2cos(3πx) - 2) - 3| - 1) - 2| - 3) + 3)) + 2| - 1, g(x) = -5((-2(2cos(3π(3|x + 3| + 1))) + 3)/(2(2cos(3π(3|x + 3| + 1)))))^2 - 3((-2(2cos(3π(3|x + 3| + 1))) + 3)/(2(2cos(3π(... | -0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3cos(3π(-1((2(2(3x - 3) + 2) - 3)/(-1(2(3x - 3) + 2))) + 1) + 2) and g(x) = 2(-3cos(3π(2|(-1x^2 - 2x + 3) + 1| - 3) - 1) - 2) - 3 from x = -4.4 to x = -4.300000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\bo... | 0.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(2|(1(-4(3|x + 2| + 2)^2 - 2(3|x + 2| + 2) - 2)^2 - 4(-4(3|x + 2| + 2)^2 - 2(3|x + 2| + 2) - 2) - 5) - 3| + 1) - 1)/(2(2|(1(-4(3|x + 2| + 2)^2 - 2(3|x + 2| + 2) - 2)^2 - 4(-4(3|x + 2| + 2)^2 - 2(3|x + 2| + 2) - 2) - 5) - 3| + 1) ... | 56.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2((3(-2((-1(-3x - 2) - 1)/(1(-3x - 2) + 3)) + 3))/(1(-2((-1(-3x - 2) - 1)/(1(-3x - 2) + 3)) + 3)))^2 + 4((3(-2((-1(-3x - 2) - 1)/(1(-3x - 2) + 3)) + 3))/(1(-2((-1(-3x - 2) - 1)/(1(-3x - 2) + 3)) + 3))) - 5, g(x) = -1(4(-3(2cos(1πx) + 3)^2 + ... | 188.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(3π(4(-5(1|(-3x + 1) + 1| - 2) - 2) + 3) - 2) - 3 and g(x) = -2|(-5(1cos(3π((-3x - 1)/(-1x + 3))))^2 + 1(1cos(3π((-3x - 1)/(-1x + 3)))) + 4) + 3| + 1 between the vertical lines x = 2.5 and x = 2.6. Round to 1 decimal place.\n\nP... | 0.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3((-1((1(-1(4x^2 + 3x - 3) - 2) + 1)/(2(-1(4x^2 + 3x - 3) - 2) + 3)) + 2)/(3((1(-1(4x^2 + 3x - 3) - 2) + 1)/(2(-1(4x^2 + 3x - 3) - 2) + 3)) - 2)) - 3)/(2((-1((1(-1(4x^2 + 3x - 3) - 2) + 1)/(2(-1(4x^2 + 3x - 3) - 2) + 3)) + 2)/(3((1... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2(3|(-1sin(1π((3x + 2)/(1x - 3)) - 2)) + 3| - 3) - 5) - 2)/(1(2(3|(-1sin(1π((3x + 2)/(1x - 3)) - 2)) + 3| - 3) - 5) - 3) and g(x) = -1|(5(-5(1|x - 2| + 1) + 3) - 4)| - 2 between the vertical lines x = 0.3 and x = 2.0. Round to 1 ... | 65.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(1((-1((-1((1x - 1)/(1x + 3)) - 2)/(2((1x - 1)/(1x + 3)) - 3)) - 2)/(1((-1((1x - 1)/(1x + 3)) - 2)/(2((1x - 1)/(1x + 3)) - 3)) + 1))^2 - 3((-1((-1((1x - 1)/(1x + 3)) - 2)/(2((1x - 1)/(1x + 3)) - 3)) - 2)/(1((-1((1x - 1)/(1x + 3)) - 2)/(2((1... | 0.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2π(3|((-1(-1((3x - 1)/(3x - 1)) + 2) + 1)/(1(-1((3x - 1)/(3x - 1)) + 2) - 3)) + 1|) + 2) + 1 and g(x) = 4((-1(2(-4x - 5) + 1) - 3)/(3(2(-4x - 5) + 1) + 3))^2 - 4((-1(2(-4x - 5) + 1) - 3)/(3(2(-4x - 5) + 1) + 3)) + 2 between th... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5(-3cos(3π(1|(-5(-5x^2 + 4x - 3)^2 + 5(-5x^2 + 4x - 3) - 4) - 2| + 1) + 3) + 2) - 1 and g(x) = -1sin(3π((-1(-4(3|x|) - 4) + 1)/(-1(-4(3|x|) - 4) + 2)) - 3) - 1 from x = -1.0 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaT... | 1.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2sin(2π(-1(-2|(2(-5x - 1)^2 + 5(-5x - 1) + 5) + 2| - 3) + 4)) - 1, g(x) = -4((2(2|(-5x^2 + 3x + 5) - 3| - 2) - 2)/(-3(2|(-5x^2 + 3x + 5) - 3| - 2)))^2 - 1((2(2|(-5x^2 + 3x + 5) - 3| - 2) - 2)/(-3(2|(-5x^2 + 3x + 5) - 3| - 2))) + 1, x = 4.8,... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -5(3|((-2(-2|(1x + 1) - 3|) - 2)/(-1(-2|(1x + 1) - 3|) + 2)) - 1|) and g(x) = (2(2|(-5(-3sin(3πx + 1) - 1)^2 - 3(-3sin(3πx + 1) - 1)) + 3| - 2) - 3)/(-1(2|(-5(-3sin(3πx + 1) - 1)^2 - 3(-3sin(3πx + 1) - 1)) + 3| - 2) + 3) from x = -4.1 to x =... | 0.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|((-1(-3sin(3π((-2((3x - 3)/(-1x - 3)) + 2)/(1((3x - 3)/(-1x - 3)) + 2)) + 2)) + 3)/(-3(-3sin(3π((-2((3x - 3)/(-1x - 3)) + 2)/(1((3x - 3)/(-1x - 3)) + 2)) + 2)) + 1)) - 1| - 3 and g(x) = 1sin(2π((-2(-2(-2|x + 3| + 3)^2 + 5(-2|x + 3| + 3) - ... | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-3|(-3(4(-2x - 4) + 5) + 1) + 3| + 1)^2 + 1(-3|(-3(4(-2x - 4) + 5) + 1) + 3| + 1) - 5 and g(x) = 2|((-2(-1|(2cos(2πx - 1) + 3) - 2| + 1) - 3)/(-1(-1|(2cos(2πx - 1) + 3) - 2| + 1) - 1)) - 1| + 1 between the vertical lines x = -1.7 ... | 13.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5(-2|(1(-3(-4x + 1)^2 - 1(-4x + 1) + 3) - 5) + 1|) - 3 and g(x) = -1(-1|(-3|(-2|x + 1| + 3) + 1| + 1) + 3| - 3)^2 + 5(-1|(-3|(-2|x + 1| + 3) + 1| + 1) + 3| - 3) - 5 from x = -0.0 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in... | 8.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(2((-1((-3(1|(1x^2 - 5x)| + 1) - 1)/(-2(1|(1x^2 - 5x)| + 1) - 2)) - 1)/(-3((-3(1|(1x^2 - 5x)| + 1) - 1)/(-2(1|(1x^2 - 5x)| + 1) - 2)) - 2))) - 1 and g(x) = -5(1(-1(-5x^2 + 1x - 1)^2 - 4(-5x^2 + 1x - 1) + 5) + 4)^2 + 2 between th... | 1.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2e^(-1(-1|((2(-2((1x - 1)/(2x - 1))^2 - 2((1x - 1)/(2x - 1)) - 3) + 2)/(1(-2((1x - 1)/(2x - 1))^2 - 2((1x - 1)/(2x - 1)) - 3) + 2)) - 3| + 2)) + 1 and g(x) = (3(-3(-2|(-3x + 3) + 1| - 2) + 1))/(-1(-3(-2|(-3x + 3) + 1| - 2) + 1) - 1) from x ... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(-5(4((-2((2x - 2)/(-3x - 2)) + 2)/(-2((2x - 2)/(-3x - 2)) - 3))^2 - 4((-2((2x - 2)/(-3x - 2)) + 2)/(-2((2x - 2)/(-3x - 2)) - 3)) - 1) - 4) + 4 and g(x) = 5((1(-2|(-1sin(1πx - 2) - 1) - 1| + 1) - 2)/(1(-2|(-1sin(1πx - 2) - 1) - 1| + 1) - 3)... | 1.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(-3|(-3cos(1π(4((-3x)/(-1x))^2 + 4((-3x)/(-1x)) + 4) + 1) - 2) + 3| - 3) - 3| and g(x) = (-3((2(-3(-3x^2 + 1x + 5) - 3))/(-1(-3(-3x^2 + 1x + 5) - 3) - 2)))/(2((2(-3(-3x^2 + 1x + 5) - 3))/(-1(-3(-3x^2 + 1x + 5) - 3) - 2)) + 1) from x = -1.3... | 52.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-5((1(-2|((-1x + 1)/(2x + 1)) - 1| + 2) - 1)/(3(-2|((-1x + 1)/(2x + 1)) - 1| + 2) - 1))^2 - 1((1(-2|((-1x + 1)/(2x + 1)) - 1| + 2) - 1)/(3(-2|((-1x + 1)/(2x + 1)) - 1| + 2) - 1)) + 4) - 2 and g(x) = 1|((-2(1cos(2π(-3x^2 - 3x - 2))... | 0.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(-4(-2|(3|(-3sin(2πx + 2) + 1) + 1| - 3)| + 2) - 2)^2 + 4(-4(-2|(3|(-3sin(2πx + 2) + 1) + 1| - 3)| + 2) - 2) + 5 and g(x) = (2(2|((3((2x + 1)/(1x + 1)) - 1)/(-2((2x + 1)/(1x + 1)) + 3)) + 1| + 1) + 1)/(-1(2|((3((2x + 1)/(1x + 1)) - 1)/(-2(... | 4.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(4(3e^(2(-4(-2|x + 2|) - 5)) - 3)^2 - 3(3e^(2(-4(-2|x + 2|) - 5)) - 3) + 1))/(-1(4(3e^(2(-4(-2|x + 2|) - 5)) - 3)^2 - 3(3e^(2(-4(-2|x + 2|) - 5)) - 3) + 1) - 3) and g(x) = 3|(2|(1(2cos(2πx + 2) + 1)^2 - 1(2cos(2πx + 2) + 1)) + 1| - 1) - 3... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3((-1(1((1(-3sin(1πx - 3)))/(-1(-3sin(1πx - 3)) + 2))^2 + 3((1(-3sin(1πx - 3)))/(-1(-3sin(1πx - 3)) + 2)) - 3) + 2)/(-3(1((1(-3sin(1πx - 3)))/(-1(-3sin(1πx - 3)) + 2))^2 + 3((1(-3sin(1πx - 3)))/(-1(-3sin(1πx - 3)) + 2)) - 3) - 1)))/(1((-1(... | 12.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|((-3(1|(5(2x + 5) - 2) + 1| + 2) - 1)/(1(1|(5(2x + 5) - 2) + 1| + 2) + 3)) - 3| + 1 and g(x) = (-3(2sin(1π(-1(4x - 1) - 3) + 3) - 2) - 1)/(1(2sin(1π(-1(4x - 1) - 3) + 3) - 2) + 1) from x = -3.0 to x = -2.8. Round to 1 decimal place.\n\nPre... | 4.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2(2((-2((3x - 1)/(-2x - 3)) - 3)/(1((3x - 1)/(-2x - 3)) + 2)) + 5)^2 + 2(2((-2((3x - 1)/(-2x - 3)) - 3)/(1((3x - 1)/(-2x - 3)) + 2)) + 5) - 1))/(1(2(2((-2((3x - 1)/(-2x - 3)) - 3)/(1((3x - 1)/(-2x - 3)) + 2)) + 5)^2 + 2(2((-2((3x... | 212.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(-3|((3(-1|(-4x + 4) + 2| + 2) - 2)/(-2(-1|(-4x + 4) + 2| + 2))) - 2| + 2) + 4, g(x) = (2(2(-2|(2x^2 - 1x + 3) + 3| + 3) - 2) - 3)/(2(2(-2|(2x^2 - 1x + 3) + 3| + 3) - 2) - 1), x = 1.9, and x = 2.0. Round your answer to 1 decimal place.\n\nP... | 16.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1cos(1π(4((-1(3|((-1x + 3)/(-2x)) + 1| + 3) + 1)/(-1(3|((-1x + 3)/(-2x)) + 1| + 3))) + 3)) - 2 and g(x) = -2|(-2|(1sin(3π((-2x + 2)/(-2x)) + 1) - 3) + 2| - 2) + 3| + 2 from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer ... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((-1(1(-2(3cos(3πx + 3) + 2)^2 - 2(3cos(3πx + 3) + 2))^2 - 5(-2(3cos(3πx + 3) + 2)^2 - 2(3cos(3πx + 3) + 2)) + 2) + 2)/(-3(1(-2(3cos(3πx + 3) + 2)^2 - 2(3cos(3πx + 3) + 2))^2 - 5(-2(3cos(3πx + 3) + 2)^2 - 2(3cos(3πx + 3) + 2)) + ... | 76.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(3(-1sin(3π(-4(3|x - 2| - 1) + 3) + 2) - 1) - 2))/(3(3(-1sin(3π(-4(3|x - 2| - 1) + 3) + 2) - 1) - 2)) and g(x) = (2((-2(2|(3cos(2πx + 3)) + 1|) + 2)/(-3(2|(3cos(2πx + 3)) + 1|) - 1)) + 2)/(1((-2(2|(3cos(2πx + 3)) + 1|) + 2)/(-3(2|(3cos(2πx... | 3.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(-5((2(3(4x - 3)^2 + 1(4x - 3) - 1) + 2)/(-2(3(4x - 3)^2 + 1(4x - 3) - 1) - 2)) - 3)^2 + 5(-5((2(3(4x - 3)^2 + 1(4x - 3) - 1) + 2)/(-2(3(4x - 3)^2 + 1(4x - 3) - 1) - 2)) - 3), g(x) = 1((-3(2e^(1(-4x^2 + 3x - 2))) + 1)/(2(2e^(1(-4x^2 + 3x - ... | 17.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3(-3|(1e^(-1(-2|((2x)/(-3x + 1)) + 3| + 2)) - 3) - 2| + 2) + 2 and g(x) = 5(2sin(3π(-1(-1x - 4) - 2)) - 2) - 4 from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 1.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(1((2(3sin(1π(3x^2 + 1x - 4) - 2) - 2) + 1)/(-1(3sin(1π(3x^2 + 1x - 4) - 2) - 2) - 1))^2 + 5((2(3sin(1π(3x^2 + 1x - 4) - 2) - 2) + 1)/(-1(3sin(1π(3x^2 + 1x - 4) - 2) - 2) - 1)) - 1) - 2, g(x) = (1(-5(4(-1x - 1)^2 + 2(-1x - 1) + 1)^2 - 3(4(... | 0.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(5(3e^(-1((2(2x + 5))/(2(2x + 5) + 3))) - 1)^2 + 4(3e^(-1((2(2x + 5))/(2(2x + 5) + 3))) - 1) + 3) + 5 and g(x) = 1(-3((3(-2x^2 + 1) + 3)/(-3(-2x^2 + 1) - 1)) + 1) between the vertical lines x = -0.8 and x = 0.8. Round to 1 decimal ... | 39.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(1|(2cos(2π(1|(-2x + 5) + 3| + 1) - 3) - 1) + 2| - 2) - 2)/(-1(1|(2cos(2π(1|(-2x + 5) + 3| + 1) - 3) - 1) + 2| - 2)) and g(x) = -3((2(-2(5x^2 - 2x)^2 + 3(5x^2 - 2x) + 4) + 2)/(2(-2(5x^2 - 2x)^2 + 3(5x^2 - 2x) + 4))) + 5 between th... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(1(-2(-5(-1sin(3πx - 1) - 2)^2 - 2(-1sin(3πx - 1) - 2)) - 4) - 5)| + 1, g(x) = -2cos(1π(2|((-1(-5x - 4) + 3)/(-2(-5x - 4) + 3)) + 3| + 3) - 2) + 3, x = 3.2, and x = 3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex ... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(2π(-4(5((-2(3|x + 1| - 1) - 1)/(-2(3|x + 1| - 1) + 3))^2 + 2((-2(3|x + 1| - 1) - 1)/(-2(3|x + 1| - 1) + 3)) - 1)^2 - 5(5((-2(3|x + 1| - 1) - 1)/(-2(3|x + 1| - 1) + 3))^2 + 2((-2(3|x + 1| - 1) - 1)/(-2(3|x + 1| - 1) + 3)) - 1) -... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(4(2sin(2π(-4(-5x^2 + 3x + 2)^2 - 5(-5x^2 + 3x + 2) - 5)) + 1)^2 - 5(2sin(2π(-4(-5x^2 + 3x + 2)^2 - 5(-5x^2 + 3x + 2) - 5)) + 1) + 5)^2 - 4(4(2sin(2π(-4(-5x^2 + 3x + 2)^2 - 5(-5x^2 + 3x + 2) - 5)) + 1)^2 - 5(2sin(2π(-4(-5x^2 + 3x + 2)^2 - ... | 18.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1|(1(3sin(2π((3x + 2)/(-2x - 1)) + 1) - 1)) - 1| - 1) + 3 and g(x) = (-1(-5(4(1x^2 + 4x + 1) + 5) - 1) - 2)/(1(-5(4(1x^2 + 4x + 1) + 5) - 1) + 1) between the vertical lines x = -0.4 and x = -0.3. Round to 1 decimal place.\n\nPres... | 0.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3|(-3((3(-1|(-1|x - 1| - 1)| - 1) + 1)/(-3(-1|(-1|x - 1| - 1)| - 1)))^2 + 2((3(-1|(-1|x - 1| - 1)| - 1) + 1)/(-3(-1|(-1|x - 1| - 1)| - 1))) + 4)| - 3, g(x) = 4((1(-2(-3cos(1πx + 3) - 2)^2 + 5(-3cos(1πx + 3) - 2) - 3) + 3)/(-1(-2(-3cos(1πx + ... | 2.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1((-3((-1(-3(-2sin(1πx - 1) - 3)^2 + 4(-2sin(1πx - 1) - 3) + 1) + 2)/(1(-3(-2sin(1πx - 1) - 3)^2 + 4(-2sin(1πx - 1) - 3) + 1) + 1)))/(-2((-1(-3(-2sin(1πx - 1) - 3)^2 + 4(-2sin(1πx - 1) - 3) + 1) + 2)/(1(-3(-2sin(1πx - 1) - 3)^2 + 4(-2sin(1π... | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(-1|(3(1sin(3π((-1x - 2)/(3x - 1))) - 3)) - 1| - 1) + 2)/(-1(-1|(3(1sin(3π((-1x - 2)/(3x - 1))) - 3)) - 1| - 1) - 2) and g(x) = (3(2(-3cos(2π(-2|x - 2| - 2) + 2) + 2) + 2) + 1)/(3(2(-3cos(2π(-2|x - 2| - 2) + 2) + 2) + 2) - 2) from x = -0.... | 1.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4((-1((1(1(5x + 1)^2 + 4(5x + 1) + 2) + 1)/(1(1(5x + 1)^2 + 4(5x + 1) + 2) + 1)) - 2)/(-1((1(1(5x + 1)^2 + 4(5x + 1) + 2) + 1)/(1(1(5x + 1)^2 + 4(5x + 1) + 2) + 1)) + 3)) - 1, g(x) = -1|(4(1(-1|x + 1| - 3)^2 + 4(-1|x + 1| - 3) - 3) + 1)| + 1... | 19.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-3((-2(-3(5x^2 - 2x + 5)^2 + 3(5x^2 - 2x + 5) + 1) - 3)/(-3(-3(5x^2 - 2x + 5)^2 + 3(5x^2 - 2x + 5) + 1) - 3))^2 - 3((-2(-3(5x^2 - 2x + 5)^2 + 3(5x^2 - 2x + 5) + 1) - 3)/(-3(-3(5x^2 - 2x + 5)^2 + 3(5x^2 - 2x + 5) + 1) - 3)) - 5) -... | 30.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(2|(1cos(3π(-2(-1x^2 + 3x - 5)^2 + 3(-1x^2 + 3x - 5) + 3) + 3) + 2) + 3| - 1) + 5 and g(x) = -2|(1sin(2π(1(-2x - 4) + 1) - 3) + 2) - 3| - 1 between the vertical lines x = -1.2 and x = -1.0999999999999999. Round to 1 decimal place.... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((-3(5(-2|(1cos(2πx + 1) - 3) + 3| + 1) - 5))/(1(5(-2|(1cos(2πx + 1) - 3) + 3| + 1) - 5)))| - 3 and g(x) = 1(2(-5(-5x^2 - 4x + 4) - 3)^2 + 5(-5(-5x^2 - 4x + 4) - 3) - 4)^2 + 4(2(-5(-5x^2 - 4x + 4) - 3)^2 + 5(-5(-5x^2 - 4x + 4) - 3... | 18.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(3π(-1|((1(1(1x^2 + 1x + 3)^2 - 4(1x^2 + 1x + 3) - 4) + 1)/(2(1(1x^2 + 1x + 3)^2 - 4(1x^2 + 1x + 3) - 4))) - 1| + 2) - 2) + 2 and g(x) = -2(-1sin(3π(-1|(3|x + 3| + 2) - 3| - 3) - 2) - 1) - 1 between the vertical lines x = -0.0 a... | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5(-1(-2|(4((3x - 1)/(-3x - 3))) + 2| + 3) - 3)^2 + 1(-1(-2|(4((3x - 1)/(-3x - 3))) + 2| + 3) - 3) + 5 and g(x) = -5((3(-4((2x - 2)/(-2x + 3))^2 + 4((2x - 2)/(-2x + 3)) - 4) - 1)/(-2(-4((2x - 2)/(-2x + 3))^2 + 4((2x - 2)/(-2x + 3)) - 4) + 1))... | -10181.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(3cos(2π(4(1(-4x^2 - 1x + 4) + 2) - 4)) - 2) - 1| and g(x) = 1(-3(-2(3|x + 2| - 3)^2 - 4(3|x + 2| - 3) + 2) + 5)^2 + 1(-3(-2(3|x + 2| - 3)^2 - 4(3|x + 2| - 3) + 2) + 5) between the vertical lines x = -3.0 and x = -2.9. Round to 1 ... | 0.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((2((3(-2cos(2π(2x + 5) - 3) - 3) - 3)/(2(-2cos(2π(2x + 5) - 3) - 3) + 2)) + 2)/(-2((3(-2cos(2π(2x + 5) - 3) - 3) - 3)/(2(-2cos(2π(2x + 5) - 3) - 3) + 2)) - 3)) + 1 and g(x) = (3(1((1(3sin(1πx - 1) - 3) - 3)/(1(3sin(1πx - 1) - 3) +... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(-1(-5(3(3x)^2 - 5(3x)) - 4) - 4)^2 - 4(-1(-5(3(3x)^2 - 5(3x)) - 4) - 4) + 1 and g(x) = (-1(-1|((3(4x - 4) - 2)/(1(4x - 4) + 3)) - 3|) + 3)/(-3(-1|((3(4x - 4) - 2)/(1(4x - 4) + 3)) - 3|) + 1) from x = 0.6 to x = 0.7. Round to 1 decimal plac... | 12.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(4(2sin(2π(-3(3|x + 1| + 3)^2 + 1(3|x + 1| + 3) + 5) - 2) - 1)^2 + 2(2sin(2π(-3(3|x + 1| + 3)^2 + 1(3|x + 1| + 3) + 5) - 2) - 1)) + 2 and g(x) = (1((1(3|(2x^2 - 4x + 5) + 1| - 1))/(2(3|(2x^2 - 4x + 5) + 1| - 1) + 3)) - 3)/(2((1(3|(2x^2 - 4... | 1.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3(1(1|(-1cos(2π(-1x^2 - 4) + 2)) - 1| + 2)) - 2 and g(x) = 2|(3|(-1|((2x - 1)/(2x + 1)) - 3|)| - 2) - 3| - 1 from x = 1.3 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(-1|((-3(5(3cos(3πx) - 2)) + 2)/(-3(5(3cos(3πx) - 2)) + 1))| - 2)^2 - 2(-1|((-3(5(3cos(3πx) - 2)) + 2)/(-3(5(3cos(3πx) - 2)) + 1))| - 2) + 3, g(x) = (-3(4(3|(-3|x + 1| + 2)| - 3) + 5) + 1)/(-2(4(3|(-3|x + 1| + 2)| - 3) + 5) - 1), x = -0.5, ... | 10.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|(3e^(-1((1((1(-1|x + 3| + 1) - 3)/(-1(-1|x + 3| + 1) - 3)) + 3)/(-1((1(-1|x + 3| + 1) - 3)/(-1(-1|x + 3| + 1) - 3)) - 3))) + 1) + 1| - 3, g(x) = 1(-3(4(-1x^2 + 4) + 3)^2 - 3(4(-1x^2 + 4) + 3) + 5)^2 + 2(-3(4(-1x^2 + 4) + 3)^2 - 3(4(-1x^2 +... | 1.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((1(2sin(1π((2(4x^2 + 3) + 3)/(-2(4x^2 + 3) - 2)) - 1) - 3) + 3)/(2(2sin(1π((2(4x^2 + 3) + 3)/(-2(4x^2 + 3) - 2)) - 1) - 3) + 3))^2 - 1((1(2sin(1π((2(4x^2 + 3) + 3)/(-2(4x^2 + 3) - 2)) - 1) - 3) + 3)/(2(2sin(1π((2(4x^2 + 3) + 3)/(... | 1.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(-2cos(1π(1|((-1(-3|x + 2| - 2))/(-3(-3|x + 2| - 2) - 3)) + 1| - 2) - 3) - 2) + 5, g(x) = -1|(-2cos(3π(-4(3x^2 - 2x + 5) + 5) + 3) + 2)| + 3, x = -2.5, and x = -2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex forma... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(2(2|(3(1e^(-2x))^2 + 4(1e^(-2x)) - 1)|) - 3) - 3)/(-3(2(2|(3(1e^(-2x))^2 + 4(1e^(-2x)) - 1)|) - 3) - 1) and g(x) = -5((-2(-3sin(2π(-5x + 2) - 3)) - 1)/(1(-3sin(2π(-5x + 2) - 3))))^2 + 5((-2(-3sin(2π(-5x + 2) - 3)) - 1)/(1(-3sin(... | 5.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4((-2(1|((1((-1x + 1)/(-3x - 3)))/(-2((-1x + 1)/(-3x - 3)) - 2)) + 2| - 1) + 1)/(-2(1|((1((-1x + 1)/(-3x - 3)))/(-2((-1x + 1)/(-3x - 3)) - 2)) + 2| - 1) - 3)) + 3 and g(x) = 3((1(-1cos(3π(3|x - 3|)) + 1) + 2)/(3(-1cos(3π(3|x - 3|)) + 1) + 3... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|((3((-1(4(-2x^2 - 4x - 3) + 2) + 3)/(-1(4(-2x^2 - 4x - 3) + 2))) - 2)/(2((-1(4(-2x^2 - 4x - 3) + 2) + 3)/(-1(4(-2x^2 - 4x - 3) + 2))) + 3))| - 3 and g(x) = 3(1|(3(-2|x| + 1)^2 - 4(-2|x| + 1) - 4) - 3| - 2) + 4 from x = -1.0 to x = -0.9. Ro... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3((-2(2|((-2(-4x^2 + 2x + 5) + 2)/(-1(-4x^2 + 2x + 5) - 3)) + 2| - 1) + 2)/(-2(2|((-2(-4x^2 + 2x + 5) + 2)/(-1(-4x^2 + 2x + 5) - 3)) + 2| - 1) + 3)) - 1 and g(x) = 3(1e^(-1(-3(5x - 2) - 2)) - 3) - 4 from x = -0.9 to x = 0.3. Round to 1 deci... | 9.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1((-1(-3cos(3π(3(2x^2 - 4x + 3)^2 - 2(2x^2 - 4x + 3) - 5) + 3) + 1) - 1)/(-2(-3cos(3π(3(2x^2 - 4x + 3)^2 - 2(2x^2 - 4x + 3) - 5) + 3) + 1) + 1)))/(-2((-1(-3cos(3π(3(2x^2 - 4x + 3)^2 - 2(2x^2 - 4x + 3) - 5) + 3) + 1) - 1)/(-2(-3cos(... | 6.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(1(-2sin(2π(-1|(-5x^2 - 2x + 3) - 3| + 2)))^2 + 1(-2sin(2π(-1|(-5x^2 - 2x + 3) - 3| + 2)))) - 2| - 1 and g(x) = 4(-2e^(-1((1((2x + 2)/(-1x - 1)) + 2)/(2((2x + 2)/(-1x - 1)) - 1))) - 1) + 5 between the vertical lines x = 1.3 and x... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3|(-2|((-2((-3(-2x^2 - 4x + 3) + 2)/(-2(-2x^2 - 4x + 3) - 2)) - 1)/(2((-3(-2x^2 - 4x + 3) + 2)/(-2(-2x^2 - 4x + 3) - 2)) - 3))| - 2) + 3|, g(x) = 2(1(5(2x^2 + 1x - 3)^2 + 1(2x^2 + 1x - 3) - 3)^2 - 2(5(2x^2 + 1x - 3)^2 + 1(2x^2 + 1x - 3) - 3)... | 86.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-2(-4((-1(-1x^2 + 4x + 2) - 2)/(-1(-1x^2 + 4x + 2) - 3))^2 + 2) + 5) - 2)/(-3(-2(-4((-1(-1x^2 + 4x + 2) - 2)/(-1(-1x^2 + 4x + 2) - 3))^2 + 2) + 5) + 1) and g(x) = -1sin(3π(-2|(1|(-5x^2 + 1x) - 2| + 1) + 2| + 2) - 1) - 1 between t... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5((2(1((3(-3x - 2) + 2)/(-2(-3x - 2))) - 5) + 2)/(2(1((3(-3x - 2) + 2)/(-2(-3x - 2))) - 5) + 3)) - 5 and g(x) = -4(5((-2(-3|x + 3| + 2) + 3)/(-1(-3|x + 3| + 2) + 2))^2 + 1) - 4 between the vertical lines x = -2.9 and x = -2.8. Roun... | 0.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|((-3(1((2((2x - 1)/(1x - 2)))/(3((2x - 1)/(1x - 2)) - 1)) + 1) - 1)/(2(1((2((2x - 1)/(1x - 2)))/(3((2x - 1)/(1x - 2)) - 1)) + 1) - 1))| - 3 and g(x) = 4((2(2|(-1|x - 2|) - 1|) + 1)/(-2(2|(-1|x - 2|) - 1|) + 3))^2 - 5((2(2|(-1|x - 2|) - 1|)... | 0.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(2|(-4(-2|(2x - 2) - 1| + 1)^2 - 1(-2|(2x - 2) - 1| + 1) + 2) - 2| + 1)^2 - 1(2|(-4(-2|(2x - 2) - 1| + 1)^2 - 1(-2|(2x - 2) - 1| + 1) + 2) - 2| + 1) + 2 and g(x) = (3(-3|(1|(-2x) + 1| - 1) + 3| + 2) + 2)/(-2(-3|(1|(-2x) + 1| - 1) ... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((-2(-2(2((1x + 3)/(3x))^2 - 1((1x + 3)/(3x)) - 4) - 4) - 1)/(-3(-2(2((1x + 3)/(3x))^2 - 1((1x + 3)/(3x)) - 4) - 4) + 1)) - 2 and g(x) = 4(-4(-1|(-2sin(2πx) + 3) - 1| + 3)^2 - 2) + 3 between the vertical lines x = -0.9 and x = 1.1.... | 106.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1e^(2(1((3(-1|(-1x^2 + 4x + 3) - 2| + 2) - 3)/(-2(-1|(-1x^2 + 4x + 3) - 2| + 2) + 1)))) + 3 and g(x) = (-3((-1(3cos(1π(-2|x - 1| - 2) + 1) - 2) + 1)/(3(3cos(1π(-2|x - 1| - 2) + 1) - 2) + 1)) + 1)/(2((-1(3cos(1π(-2|x - 1| - 2) + 1) ... | 2.3 | MATH |
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