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Problem 25 Easy Difficulty

Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line.
$$y=\sin ^{2} x, y=0,0 \leqslant x \leqslant \pi ; \quad \text { about } y=-1$$

Answer

$$
V=\frac{11 \pi^{2}}{8}
$$

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Video Transcript

Okay, So for this problem, when you're asked to find the volume with an outer radius, which of course, is gonna be the upper boundary of one plus sine squared X and then our inner or are lower boundary is going to be one. And we're going on x between pie and zero. And so, of course, since we have two different radio I we want to look at the washer method. So using the washer, we're gonna have the volume equals pi oven integral from a to B of our one squared minus are two squared DX. So what I want to do is I want to set this up so it's gonna be pi from the integral of pied a zero of one plus sign X or sine squared x and then all of that squared minus one squared, which would be one DX. So we're supposed to be utilizing a calculator to get the approximation. So this is going to be 11. Pi squared over eight, which is approximately 13.5707

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