messages listlengths 3 3 | topic stringclasses 1
value | subtopic stringclasses 14
values |
|---|---|---|
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (-2 x)$ on the interval $x = 1$ to $x = 11$"
},
{
"role": "assistant",
"content": "$\\sqrt{2} \\left(\\sq... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos \\left(\\frac{9 x}{2}\\right)$ on the interval $x = 2$ to $x = 2$"
},
{
"role": "assistant",
"content": "... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sin ^{-1}\\left(\\frac{5 x}{2}\\right)-\\log \\left(-4 x^4\\right)$ on the interval $x = 4$ to $x = 6$"
},
{
"rol... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos (x)$ on the interval $x = 4$ to $x = 12$"
},
{
"role": "assistant",
"content": "$4 E(-1)+E(12-3 \\pi |-1)... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos (3 x)$ on the interval $x = 2$ to $x = 6$"
},
{
"role": "assistant",
"content": "$\\frac{1}{3} (6 E(-9)+E... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\tan (2 x)$ on the interval $x = 3$ to $x = 3$"
},
{
"role": "assistant",
"content": "$0$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sqrt{x}$ on the interval $x = 5$ to $x = 9$"
},
{
"role": "assistant",
"content": "$\\frac{1}{8} \\left(12 \\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (5 x)$ on the interval $x = 0$ to $x = 10$"
},
{
"role": "assistant",
"content": "$\\int_0^{10} \\sqrt{\\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos (3 x)$ on the interval $x = 1$ to $x = 5$"
},
{
"role": "assistant",
"content": "$\\frac{1}{3} (6 E(-9)-E... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\tan (x)$ on the interval $x = 0$ to $x = 7$"
},
{
"role": "assistant",
"content": "$\\int_0^7 \\sqrt{\\sec ^... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -2^{2/3} \\sqrt[3]{x^2}$ on the interval $x = 5$ to $x = 13$"
},
{
"role": "assistant",
"content": "$\\frac{1}{... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cosh (4 x)$ on the interval $x = 1$ to $x = 9$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} i (E(4 i|... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos (2 x)$ on the interval $x = 5$ to $x = 8$"
},
{
"role": "assistant",
"content": "$E(-4)+\\frac{1}{2} (E(1... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sqrt{x}$ on the interval $x = 4$ to $x = 9$"
},
{
"role": "assistant",
"content": "$\\frac{1}{8} \\left(-8 \\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\sin \\left(\\frac{21 x}{5}\\right)$ on the interval $x = 3$ to $x = 3$"
},
{
"role": "assistant",
"content":... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = 1$ on the interval $x = 5$ to $x = 15$"
},
{
"role": "assistant",
"content": "$10$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sqrt[3]{5} \\sqrt[3]{x}+\\cos (4 x)$ on the interval $x = 5$ to $x = 5$"
},
{
"role": "assistant",
"content":... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (-2 x)$ on the interval $x = 5$ to $x = 5$"
},
{
"role": "assistant",
"content": "$0$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sqrt{3} \\sqrt{-x^5}$ on the interval $x = 0$ to $x = 4$"
},
{
"role": "assistant",
"content": "$4 \\, _2F_1\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos (2 x)$ on the interval $x = 0$ to $x = 0$"
},
{
"role": "assistant",
"content": "$0$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = x^4$ on the interval $x = 1$ to $x = 1$"
},
{
"role": "assistant",
"content": "$0$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\tan \\left(2 x^3\\right)$ on the interval $x = 4$ to $x = 4$"
},
{
"role": "assistant",
"content": "$0$"
}
... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sqrt{3} \\sqrt{x}$ on the interval $x = 2$ to $x = 2$"
},
{
"role": "assistant",
"content": "$0$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos (x)$ on the interval $x = 4$ to $x = 13$"
},
{
"role": "assistant",
"content": "$4 E(-1)+E(13-3 \\pi |-1)... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sqrt{3} \\sqrt{-x}$ on the interval $x = 1$ to $x = 6$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} \... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\sin (4 x)$ on the interval $x = 0$ to $x = 8$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} \\sqrt{17... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\frac{1}{8 x^3}$ on the interval $x = 0$ to $x = 4$"
},
{
"role": "assistant",
"content": "$\\int_0^4 \\sqrt{... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\frac{2 \\log (2 x)}{\\pi }$ on the interval $x = 0$ to $x = 9$"
},
{
"role": "assistant",
"content": "$\\int_... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -x$ on the interval $x = 4$ to $x = 6$"
},
{
"role": "assistant",
"content": "$2 \\sqrt{2}$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sqrt[3]{x}$ on the interval $x = 3$ to $x = 3$"
},
{
"role": "assistant",
"content": "$0$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\tan (3 x)$ on the interval $x = 4$ to $x = 11$"
},
{
"role": "assistant",
"content": "$\\int_4^{11} \\sqrt{9 ... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (4 x)-\\cos ^{-1}(5 x)$ on the interval $x = 0$ to $x = 3$"
},
{
"role": "assistant",
"content": "$\\int_... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -2 x$ on the interval $x = 0$ to $x = 3$"
},
{
"role": "assistant",
"content": "$3 \\sqrt{5}$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = e^{-x}$ on the interval $x = 1$ to $x = 5$"
},
{
"role": "assistant",
"content": "$\\frac{\\sqrt{1+e^2}}{e}-\\f... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\tan \\left(\\frac{9 x}{2}\\right)$ on the interval $x = 3$ to $x = 13$"
},
{
"role": "assistant",
"content":... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = 1$ on the interval $x = 5$ to $x = 5$"
},
{
"role": "assistant",
"content": "$0$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\tan ^{-1}(2 x)$ on the interval $x = 3$ to $x = 12$"
},
{
"role": "assistant",
"content": "$\\int_3^{12} \\sq... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (-3 x)$ on the interval $x = 1$ to $x = 7$"
},
{
"role": "assistant",
"content": "$4 \\sqrt{2}+\\tanh ^{-... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (4 x)$ on the interval $x = 0$ to $x = 1$"
},
{
"role": "assistant",
"content": "$\\int_0^1 \\sqrt{\\frac... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\tanh ^{-1}\\left(\\frac{6 x^2}{5}\\right)-\\tan (x)$ on the interval $x = 0$ to $x = 0$"
},
{
"role": "assistant"... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos (x)$ on the interval $x = 3$ to $x = 5$"
},
{
"role": "assistant",
"content": "$E(5|-1)-E(3|-1)$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\infty$ on the interval $x = 1$ to $x = 7$"
},
{
"role": "assistant",
"content": "$\\text{ArcLength}[-\\infty... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos (4 x)$ on the interval $x = 5$ to $x = 9$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} (10 E(-16)... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos (5 x)$ on the interval $x = 1$ to $x = 5$"
},
{
"role": "assistant",
"content": "$\\frac{1}{5} (12 E(-25)... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\frac{38416 x^4}{625}$ on the interval $x = 0$ to $x = 4$"
},
{
"role": "assistant",
"content": "$4 \\, _2F_1\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = 1$ on the interval $x = 0$ to $x = 2$"
},
{
"role": "assistant",
"content": "$2$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (-x)$ on the interval $x = 2$ to $x = 10$"
},
{
"role": "assistant",
"content": "$-\\sqrt{5}+\\sqrt{101}+... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sin (2 x)$ on the interval $x = 0$ to $x = 1$"
},
{
"role": "assistant",
"content": "$\\frac{1}{2} \\sqrt{5} ... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (-2 x)$ on the interval $x = 5$ to $x = 12$"
},
{
"role": "assistant",
"content": "$-\\sqrt{26}+\\sqrt{14... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log \\left(-\\frac{18 x}{5}\\right)+\\log \\left(\\frac{22 x}{5}\\right)$ on the interval $x = 0$ to $x = 1$"
},
{
... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos (2 x)$ on the interval $x = 5$ to $x = 10$"
},
{
"role": "assistant",
"content": "$\\frac{1}{2} (6 E(-4)+... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = e^{2 x^4}$ on the interval $x = 4$ to $x = 12$"
},
{
"role": "assistant",
"content": "$\\int_4^{12} \\sqrt{64 e... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos (3 x)$ on the interval $x = 3$ to $x = 4$"
},
{
"role": "assistant",
"content": "$\\frac{1}{3} (E(12-2 \\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (-3 x)$ on the interval $x = 5$ to $x = 11$"
},
{
"role": "assistant",
"content": "$-\\sqrt{26}+\\sqrt{12... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\frac{81 x^2}{4}$ on the interval $x = 1$ to $x = 10$"
},
{
"role": "assistant",
"content": "$-\\frac{\\sqrt{6... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\tan (2 x)$ on the interval $x = 2$ to $x = 11$"
},
{
"role": "assistant",
"content": "$\\int_2^{11} \\sqrt{4... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\infty$ on the interval $x = 1$ to $x = 1$"
},
{
"role": "assistant",
"content": "$\\text{ArcLength}[-\\infty... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\tanh ^{-1}(x)$ on the interval $x = 3$ to $x = 8$"
},
{
"role": "assistant",
"content": "$\\int_3^8 \\sqrt{\\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sqrt[3]{\\frac{7}{2}} \\sqrt[3]{x}$ on the interval $x = 0$ to $x = 2$"
},
{
"role": "assistant",
"content": ... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\tan (2 x)$ on the interval $x = 1$ to $x = 1$"
},
{
"role": "assistant",
"content": "$0$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (2 x)$ on the interval $x = 4$ to $x = 5$"
},
{
"role": "assistant",
"content": "$-\\sqrt{17}+\\sqrt{26}+... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = e^{2 x}+\\tan ^{-1}(2 x)$ on the interval $x = 5$ to $x = 15$"
},
{
"role": "assistant",
"content": "$\\int_5^{... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = 27 x^3$ on the interval $x = 0$ to $x = 1$"
},
{
"role": "assistant",
"content": "$\\, _2F_1\\left(-\\frac{1}{2... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos (2 x)$ on the interval $x = 3$ to $x = 6$"
},
{
"role": "assistant",
"content": "$E(-4)+\\frac{1}{2} (E(1... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (x)$ on the interval $x = 3$ to $x = 4$"
},
{
"role": "assistant",
"content": "$-\\sqrt{10}+\\sqrt{17}+\\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\sin (3 x)$ on the interval $x = 0$ to $x = 3$"
},
{
"role": "assistant",
"content": "$\\frac{1}{3} \\sqrt{10... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = 1$ on the interval $x = 3$ to $x = 3$"
},
{
"role": "assistant",
"content": "$0$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos (5 x)$ on the interval $x = 1$ to $x = 10$"
},
{
"role": "assistant",
"content": "$\\frac{1}{5} (28 E(-25... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos \\left(\\frac{7 x}{2}\\right)$ on the interval $x = 0$ to $x = 0$"
},
{
"role": "assistant",
"content": "... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\tan ^{-1}\\left(3 x^5\\right)$ on the interval $x = 3$ to $x = 5$"
},
{
"role": "assistant",
"content": "$\\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (4 x)$ on the interval $x = 5$ to $x = 5$"
},
{
"role": "assistant",
"content": "$0$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\tan ^{-1}\\left(x^4\\right)$ on the interval $x = 2$ to $x = 7$"
},
{
"role": "assistant",
"content": "$\\in... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (-3 x)$ on the interval $x = 5$ to $x = 14$"
},
{
"role": "assistant",
"content": "$-\\sqrt{26}+\\sqrt{19... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\tanh ^{-1}(x)$ on the interval $x = 2$ to $x = 7$"
},
{
"role": "assistant",
"content": "$\\int_2^7 \\sqrt{\\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sqrt{3} \\sqrt{-x}$ on the interval $x = 4$ to $x = 4$"
},
{
"role": "assistant",
"content": "$0$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = 1$ on the interval $x = 4$ to $x = 14$"
},
{
"role": "assistant",
"content": "$10$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\tan (x)$ on the interval $x = 5$ to $x = 10$"
},
{
"role": "assistant",
"content": "$\\int_5^{10} \\sqrt{\\s... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\tan ^{-1}(4 x)$ on the interval $x = 4$ to $x = 8$"
},
{
"role": "assistant",
"content": "$\\int_4^8 \\sqrt{\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\frac{1}{x^5}$ on the interval $x = 0$ to $x = 2$"
},
{
"role": "assistant",
"content": "$\\int_0^2 \\sqrt{\\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (-4 x)$ on the interval $x = 0$ to $x = 6$"
},
{
"role": "assistant",
"content": "$\\int_0^6 \\sqrt{\\fra... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = e^{4 x} \\cos (5 x)$ on the interval $x = 1$ to $x = 1$"
},
{
"role": "assistant",
"content": "$0$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cosh (4 x)$ on the interval $x = 1$ to $x = 7$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} i (E(4 i|... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\sqrt[3]{3} \\sqrt[3]{x}$ on the interval $x = 2$ to $x = 2$"
},
{
"role": "assistant",
"content": "$0$"
}
... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\frac{\\pi }{2}$ on the interval $x = 1$ to $x = 11$"
},
{
"role": "assistant",
"content": "$10$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = 2 \\sqrt{-x}$ on the interval $x = 2$ to $x = 7$"
},
{
"role": "assistant",
"content": "$-\\sqrt{2}+\\sqrt{42}-... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\tan (2 x)$ on the interval $x = 2$ to $x = 9$"
},
{
"role": "assistant",
"content": "$\\int_2^9 \\sqrt{4 \\s... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\sin \\left(3 x^3\\right)$ on the interval $x = 5$ to $x = 10$"
},
{
"role": "assistant",
"content": "$\\int_... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\tan ^{-1}(4 x)$ on the interval $x = 1$ to $x = 8$"
},
{
"role": "assistant",
"content": "$\\int_1^8 \\sqrt{\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (-4 x)$ on the interval $x = 4$ to $x = 12$"
},
{
"role": "assistant",
"content": "$-\\sqrt{17}+\\sqrt{14... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = 1$ on the interval $x = 3$ to $x = 10$"
},
{
"role": "assistant",
"content": "$7$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log \\left(-\\frac{9 x^2}{2}\\right)$ on the interval $x = 2$ to $x = 6$"
},
{
"role": "assistant",
"content"... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log \\left(-\\frac{7 x}{5}\\right)+\\log (-x)$ on the interval $x = 0$ to $x = 6$"
},
{
"role": "assistant",
... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log \\left(\\frac{7 x}{2}\\right)+\\cos \\left(\\frac{3 x}{2}\\right)$ on the interval $x = 0$ to $x = 4$"
},
{
"... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\infty$ on the interval $x = 1$ to $x = 10$"
},
{
"role": "assistant",
"content": "$\\text{ArcLength}[-\\inft... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = e^{-5 x} \\tan (x)$ on the interval $x = 3$ to $x = 3$"
},
{
"role": "assistant",
"content": "$0$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sqrt[3]{\\frac{5}{3}} \\sqrt[3]{x}$ on the interval $x = 0$ to $x = 5$"
},
{
"role": "assistant",
"content": ... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = 1$ on the interval $x = 4$ to $x = 7$"
},
{
"role": "assistant",
"content": "$3$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\tan (x)$ on the interval $x = 4$ to $x = 8$"
},
{
"role": "assistant",
"content": "$\\int_4^8 \\sqrt{\\sec ^... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\frac{1}{x^5}$ on the interval $x = 0$ to $x = 8$"
},
{
"role": "assistant",
"content": "$\\int_0^8 \\sqrt{\\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\tan (3 x)$ on the interval $x = 4$ to $x = 8$"
},
{
"role": "assistant",
"content": "$\\int_4^8 \\sqrt{9 \\se... | calculus | arclength |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.