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

Answer 1

Christopher Allers

Find #int_0^pi sqrt(1+(dy/dx)^2) dx#

#dy/dx = sinx+xcosx#, so we need

#int_0^pi sqrt(1+(sinx+xcosx)^2) dx# which is about #5.04#

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Answer 2

Ezekiel Alexander

To find the arc length of the curve ( y = x \sin x ) over the interval ([0, \pi]), you can use the formula for arc length:

[ L = \int_{a}^{b} \sqrt{1 + \left( \frac{dy}{dx} \right)^2} , dx ]

where ( a ) and ( b ) are the limits of integration. In this case, ( a = 0 ) and ( b = \pi ). Differentiate ( y = x \sin x ) to find ( \frac{dy}{dx} ) and substitute into the formula to evaluate the integral.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.