# 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.$$y=\sin ^{2} x, y=0,0 \leqslant x \leqslant \pi ; \quad \text { about } y=-1$$

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

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Applications of Integration

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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

#### Topics

Applications of Integration

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