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Problem 20 Easy Difficulty

Refer to the figure and find the volume generated by rotating the given region about the specified line.

$ \Re_1 $ about $ OC $

Answer

$\frac{2 \pi}{3}$

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Video Transcript

we're gonna be funding the volume Hammer would be interning along the axis peril, the axis of rotation. Which means the first thing we know is that our limits of integration are from zero on the bottom toe, one on the top and we have pie on the outside. And then we have the one squared minus y squared because it's why one ours are one minus are, too, and they're both squared individually. Find the integral, which means use the power rule, increase the expert by one and then divide by the new exponents and then pull again.