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 $f(x) = e^{-x}-\\sin ^{-1}(2 x)$ on the interval $x = 2$ to $x = 4$"
},
{
"role": "assistant",
"content": "$\\int_2^4 \... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\sqrt[3]{2} \\sqrt[3]{x}$ on the interval $x = 0$ to $x = 10$"
},
{
"role": "assistant",
"content": "$2^{2/3}... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\tanh ^{-1}(4 x)$ on the interval $x = 0$ to $x = 6$"
},
{
"role": "assistant",
"content": "$\\int_0^6 \\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 $f(x) = \\sqrt{x}$ on the interval $x = 5$ to $x = 11$"
},
{
"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 $f(x) = -3 x$ 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 $f(x) = \\cos (2 x)$ 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 $f(x) = \\cosh \\left(\\frac{5 x}{2}\\right)$ 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 $f(x) = e^{-4 x^3}$ on the interval $x = 2$ to $x = 10$"
},
{
"role": "assistant",
"content": "$\\int_2^{10} \\sqrt{144... | 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 $x = 2$ to $x = 7$"
},
{
"role": "assistant",
"content": "$5$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\sqrt[3]{x}$ on the interval $x = 0$ to $x = 2$"
},
{
"role": "assistant",
"content": "$\\sqrt[3]{2} \\, _2F_... | 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 $x = 4$ to $x = 13$"
},
{
"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 $f(x) = \\text{ComplexInfinity}$ on the interval $x = 1$ to $x = 5$"
},
{
"role": "assistant",
"content": "$\\text{ArcL... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sqrt{\\frac{5}{2}} \\sqrt{-x}$ on the interval $x = 1$ to $x = 10$"
},
{
"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 $x = 1$ to $x = 4$"
},
{
"role": "assistant",
"content": "$-\\sqrt{2}+\\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 $f(x) = \\log \\left(\\frac{14 x}{3}\\right)$ on the interval $x = 1$ to $x = 10$"
},
{
"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 $f(x) = -\\sqrt[3]{5} \\sqrt[3]{x^2}$ 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 $f(x) = 2 \\sqrt{-x}$ on the interval $x = 1$ to $x = 4$"
},
{
"role": "assistant",
"content": "$2 \\sqrt{3}+i \\cos ^{... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log \\left(-\\frac{7 x}{2}\\right)$ on the interval $x = 2$ 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 $f(x) = e^{x^4}$ on the interval $x = 2$ to $x = 6$"
},
{
"role": "assistant",
"content": "$\\int_2^6 \\sqrt{16 e^{2 x^... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos ^{-1}(2 x)$ on the interval $x = 3$ to $x = 5$"
},
{
"role": "assistant",
"content": "$\\frac{1}{2} \\sqr... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log \\left(-2 x^4\\right)$ on the interval $x = 4$ to $x = 7$"
},
{
"role": "assistant",
"content": "$-4 \\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 $f(x) = 16 x^2$ on the interval $x = 1$ to $x = 6$"
},
{
"role": "assistant",
"content": "$\\frac{1}{64} \\left(-160 \\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sin (x)$ on the interval $x = 4$ to $x = 7$"
},
{
"role": "assistant",
"content": "$\\sqrt{2} \\left(E\\left(... | 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 $x = 12$"
},
{
"role": "assistant",
"content": "$8$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\sin (5 x)$ 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 $f(x) = \\cosh (4 x)$ on the interval $x = 2$ to $x = 12$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} i (E(8 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 $f(x) = 2 \\sqrt{x}$ 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 $f(x) = \\log (3 x)$ on the interval $x = 4$ to $x = 6$"
},
{
"role": "assistant",
"content": "$-\\sqrt{17}+\\sqrt{37}+... | 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 $f(x) = -\\sin (3 x)$ 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 $f(x) = e^{-3 x}$ 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 $f(x) = 1$ on the interval $x = 2$ to $x = 3$"
},
{
"role": "assistant",
"content": "$1$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\log (-3 x)$ on the interval $x = 4$ to $x = 6$"
},
{
"role": "assistant",
"content": "$-\\sqrt{17}+\\sqrt{37}... | 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 $x = 2$ to $x = 5$"
},
{
"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 $f(x) = \\tan (4 x)$ on the interval $x = 5$ to $x = 7$"
},
{
"role": "assistant",
"content": "$\\int_5^7 \\sqrt{16 \\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 $f(x) = \\log (2 x)$ 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 $f(x) = -\\sqrt[3]{2} \\sqrt[3]{x}$ on the interval $x = 0$ to $x = 4$"
},
{
"role": "assistant",
"content": "$2 \\, _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 $f(x) = \\tan (x)$ on the interval $x = 3$ to $x = 11$"
},
{
"role": "assistant",
"content": "$\\int_3^{11} \\sqrt{\\se... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos (x)+1$ on the interval $x = 2$ to $x = 3$"
},
{
"role": "assistant",
"content": "$E(3|-1)-E(2|-1)$"
}
] | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = -\\tanh ^{-1}(x)$ on the interval $x = 2$ to $x = 9$"
},
{
"role": "assistant",
"content": "$\\int_2^9 \\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 $f(x) = \\sqrt{3} \\sqrt{-x}+1$ on the interval $x = 2$ to $x = 12$"
},
{
"role": "assistant",
"content": "$-\\sqrt{\\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 $f(x) = \\log (-5 x)$ on the interval $x = 2$ to $x = 6$"
},
{
"role": "assistant",
"content": "$-\\sqrt{5}+\\sqrt{37}+... | 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 $x = 9$"
},
{
"role": "assistant",
"content": "$5 E(-4)+\\frac{1}{2} 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 $f(x) = -\\sin (x)$ on the interval $x = 3$ to $x = 6$"
},
{
"role": "assistant",
"content": "$\\sqrt{2} \\left(E\\left... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\tanh ^{-1}(2 x)$ on the interval $x = 2$ to $x = 11$"
},
{
"role": "assistant",
"content": "$\\int_2^{11} \\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 $f(x) = \\log \\left(\\frac{9 x}{2}\\right)$ on the interval $x = 2$ to $x = 7$"
},
{
"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 $f(x) = \\tanh ^{-1}\\left(3 x^4\\right)$ on the interval $x = 0$ to $x = 4$"
},
{
"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 $f(x) = -\\tan ^{-1}\\left(2 x^2\\right)$ 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 $f(x) = -\\tan (2 x)$ on the interval $x = 5$ to $x = 9$"
},
{
"role": "assistant",
"content": "$\\int_5^9 \\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 $f(x) = -\\infty$ on the interval $x = 5$ 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 $f(x) = \\sqrt{-x}$ on the interval $x = 4$ to $x = 6$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} \\left(-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 $f(x) = \\cos \\left(\\frac{7 x}{2}\\right)$ 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 $f(x) = \\log (-2 x)$ on the interval $x = 0$ to $x = 9$"
},
{
"role": "assistant",
"content": "$\\int_0^9 \\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 $f(x) = 1$ 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 $f(x) = \\log (x)$ on the interval $x = 4$ to $x = 14$"
},
{
"role": "assistant",
"content": "$-\\sqrt{17}+\\sqrt{197}+... | 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 $x = 3$ to $x = 5$"
},
{
"role": "assistant",
"content": "$2 \\sqrt{5}-\\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 $f(x) = \\tan (x)$ 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 $f(x) = \\log (-4 x)$ on the interval $x = 1$ to $x = 5$"
},
{
"role": "assistant",
"content": "$-\\sqrt{2}+\\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 $f(x) = \\cos ^{-1}(-2 x)$ on the interval $x = 5$ to $x = 8$"
},
{
"role": "assistant",
"content": "$\\frac{1}{2} \\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 $f(x) = \\tan (4 x)$ on the interval $x = 2$ to $x = 4$"
},
{
"role": "assistant",
"content": "$\\int_2^4 \\sqrt{16 \\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 $f(x) = e^{-x}$ on the interval $x = 5$ to $x = 15$"
},
{
"role": "assistant",
"content": "$\\frac{\\sqrt{1+e^{10}}}{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 $f(x) = e^{-x}$ on the interval $x = 3$ to $x = 7$"
},
{
"role": "assistant",
"content": "$\\frac{\\sqrt{1+e^6}}{e^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 $f(x) = \\cos (4 x)$ on the interval $x = 3$ to $x = 9$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} (14 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 $f(x) = 2 \\sqrt{x}$ on the interval $x = 4$ to $x = 13$"
},
{
"role": "assistant",
"content": "$-2 \\sqrt{5}+\\sqrt{18... | 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 $x = 0$"
},
{
"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 $f(x) = \\cos (4 x)$ on the interval $x = 1$ to $x = 3$"
},
{
"role": "assistant",
"content": "$E(-16)+\\frac{1}{4} (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 $f(x) = -\\tan (4 x)$ on the interval $x = 3$ to $x = 11$"
},
{
"role": "assistant",
"content": "$\\int_3^{11} \\sqrt{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 $f(x) = -\\sin (2 x)$ on the interval $x = 0$ to $x = 3$"
},
{
"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 $f(x) = -\\tanh ^{-1}(2 x)$ on the interval $x = 2$ to $x = 3$"
},
{
"role": "assistant",
"content": "$\\int_2^3 \\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 $f(x) = \\frac{3^{2/3} \\sqrt[3]{x}}{\\sqrt[3]{2}}$ on the interval $x = 0$ to $x = 2$"
},
{
"role": "assistant",
"cont... | 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 $x = 3$ to $x = 11$"
},
{
"role": "assistant",
"content": "$-\\sqrt{1+e^6}+\\sqrt{1+e^{22}... | 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 $x = 0$ to $x = 10$"
},
{
"role": "assistant",
"content": "$6 E(-1)+E(10-3 \\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 $f(x) = 1$ 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 $f(x) = \\tan (5 x)$ on the interval $x = 4$ to $x = 7$"
},
{
"role": "assistant",
"content": "$\\int_4^7 \\sqrt{25 \\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 $f(x) = \\sqrt{-x}$ 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 $f(x) = \\frac{\\sqrt{-x}}{\\sqrt{2}}$ on the interval $x = 2$ to $x = 9$"
},
{
"role": "assistant",
"content": "$\\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 $f(x) = \\cos (4 x)$ on the interval $x = 2$ to $x = 8$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} (14 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 $f(x) = \\cos (4 x)$ on the interval $x = 3$ to $x = 11$"
},
{
"role": "assistant",
"content": "$\\frac{1}{4} (20 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 $f(x) = \\tan (2 x)$ on the interval $x = 3$ to $x = 7$"
},
{
"role": "assistant",
"content": "$\\int_3^7 \\sqrt{4 \\se... | 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 $x = 1$ to $x = 10$"
},
{
"role": "assistant",
"content": "$-\\sqrt{2}+\\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 $f(x) = -e^{-x^2} \\sin (x)$ 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 $f(x) = -\\tan (4 x)$ on the interval $x = 1$ to $x = 6$"
},
{
"role": "assistant",
"content": "$\\int_1^6 \\sqrt{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 $f(x) = \\cos (2 x)$ 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 $f(x) = 2 \\sqrt{-x}$ on the interval $x = 1$ to $x = 9$"
},
{
"role": "assistant",
"content": "$6 \\sqrt{2}+i \\cos ^{... | 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 $x = 5$ 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 $f(x) = \\cosh ^{-1}(-2 x)$ 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 $f(x) = \\log \\left(\\frac{x}{3}\\right)$ on the interval $x = 4$ to $x = 10$"
},
{
"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 $f(x) = e^{x^4}$ on the interval $x = 4$ to $x = 10$"
},
{
"role": "assistant",
"content": "$\\int_4^{10} \\sqrt{16 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 $f(x) = -\\sqrt[3]{x}$ on the interval $x = 1$ to $x = 8$"
},
{
"role": "assistant",
"content": "$2 \\, _2F_1\\left(-\\... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\text{ComplexInfinity}$ on the interval $x = 5$ to $x = 8$"
},
{
"role": "assistant",
"content": "$\\text{ArcL... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\cos ^{-1}(-2 x)$ on the interval $x = 3$ to $x = 5$"
},
{
"role": "assistant",
"content": "$\\frac{1}{2} \\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 $f(x) = \\tan (4 x)$ on the interval $x = 4$ to $x = 7$"
},
{
"role": "assistant",
"content": "$\\int_4^7 \\sqrt{16 \\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 $f(x) = \\log (4 x)$ on the interval $x = 3$ to $x = 12$"
},
{
"role": "assistant",
"content": "$-\\sqrt{10}+\\sqrt{145... | 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 $x = 0$ to $x = 4$"
},
{
"role": "assistant",
"content": "$2 E(-1)+E(4-\\pi |-1)$"
... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = \\sqrt{2} e^x \\sqrt{x}$ on the interval $x = 1$ to $x = 5$"
},
{
"role": "assistant",
"content": "$\\int_1^5 \... | calculus | arclength |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the arclength of the function $f(x) = e^{-3 x} \\sin \\left(4 x^4\\right)$ 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 $f(x) = \\cos (4 x)$ on the interval $x = 3$ to $x = 7$"
},
{
"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 $f(x) = -\\sqrt[3]{3} \\sqrt[3]{x}$ 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 $x = 0$ to $x = 7$"
},
{
"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 $f(x) = -\\frac{17 x}{5}$ on the interval $x = 3$ to $x = 11$"
},
{
"role": "assistant",
"content": "$\\frac{8 \\sqrt{3... | calculus | arclength |
End of preview. Expand in Data Studio
Khan Math – Calculus
Calculus problems from Khan Academy in ChatML format. Covers derivatives, integrals, series, vector calculus, and more.
Quick Start
from datasets import load_dataset
dataset = load_dataset("NecroMOnk/khan-math-calculus")
print(dataset["train"][0])
Example record:
{
"messages": [
{"role": "system", "content": "You are a mathematics tutor. Answer the following math problem."},
{"role": "user", "content": "Find the arclength of the function $f(x) = \\log(2x)$ on the interval $x=4$ to $x=5$"},
{"role": "assistant", "content": "$-\\sqrt{17}+\\sqrt{26}+\\tanh^{-1}\\left(\\sqrt{17}\\right)-\\tanh^{-1}\\left(\\sqrt{26}\\right)$"}
],
"topic": "calculus",
"subtopic": "arclength"
}
Dataset Stats
- 540K problems
- ChatML format
- Source: Khan Academy calculus materials
- Language: English
- Math notation: LaTeX
Fields
| Field | Type | Description |
|---|---|---|
messages |
list | ChatML turns: system, user, assistant |
topic |
string | Top-level math topic (e.g. calculus) |
subtopic |
string | Specific subtopic (e.g. arclength) |
Source
Problems sourced from Khan Academy via the AMPS dataset. Problems and answers are in LaTeX format.
Versions
- v1 – raw extraction, minor artifacts possible (e.g. degenerate intervals,
+-notation) - v2 – cleaned formulas, extraction artifacts removed (coming soon)
- Downloads last month
- 11