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A-curve-is-defined-by-f-x-What-is-the-length-of-curve-from-x-a-to-x-b-

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Question Number 3291 by Rasheed Soomro last updated on 09/Dec/15
A curve is defined by f(x).What is the length of curve from x=a to x=b ?
$$\mathcal{A}\:{curve}\:{is}\:{defined}\:\:{by}\:{f}\left({x}\right).\mathcal{W}{hat}\:{is}\:{the}\:{length} \\ $$$${of}\:{curve}\:{from}\:{x}={a}\:\:{to}\:\:{x}={b}\:? \\ $$
Answered by 123456 last updated on 09/Dec/15
if f is differentiable ∫_a ^b (√(1+((df/dx))^2 ))dx
$$\mathrm{if}\:{f}\:\mathrm{is}\:\mathrm{differentiable} \\ $$$$\underset{{a}} {\overset{{b}} {\int}}\sqrt{\mathrm{1}+\left(\frac{{df}}{{dx}}\right)^{\mathrm{2}} }{dx} \\ $$
Commented by Rasheed Soomro last updated on 09/Dec/15
TH𝛂nK^S !
$$\mathcal{TH}\boldsymbol{\alpha}{n}\mathcal{K}^{\mathcal{S}} \:! \\ $$

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