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[ { "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