How do you find the arc length of the curve $y = x sin x$ $y=xsinx$ over the interval [0,pi]?

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Answer 1 · 2018-03-21T20:04:54

Find $\int_{0}^{π} \sqrt{1 + {(\frac{d y}{d x})}^{2}} d x$ $int_0^pi sqrt(1+(dy/dx)^2) dx$

$\frac{d y}{d x} = sin x + x cos x$ $dy/dx = sinx+xcosx$ , so we need

$\int_{0}^{π} \sqrt{1 + {(sin x + x cos x)}^{2}} d x$ $int_0^pi sqrt(1+(sinx+xcosx)^2) dx$ which is about $5.04$ $5.04$

How do you find the arc length of the curve y=xsinxy=xsinxy=xsinx over the interval [0,pi]?