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Problem 37 Hard 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 \le x \le \pi $ ; about $ y = -1 $

Answer

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

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Video Transcript

this problem is specified that we should draw a diagram. This is actually pretty straightforward diagram, because we know that we have 00 at the origin for one intersection point and then pi over zero intersects the graph at pie. Okay, now that we've gotten this, we know you can put into the formula vehicles pi times the integral from zero to pot of out already squared, minus in a radius squared DX. Okay, the out already it's we know is one plus sign squared acts squared because remember each radius squared minus the inter radius, which is one squared as the problem is specified To use a calculator, we end up with this value And this is also known as 11 pi squared, divided by eight.