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Problem 21 Medium Difficulty

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

$ \Re_1 $ about $ AB $


$\frac{1}{3} \pi$

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Video Transcript

Okay. In order to find the volume, we know that we're integrating along the parallel access to the axis of rotation. We know we have The radius is one minus. Y is equivalent to our therefore V is hi times, integral from 01 of the radius, which we said was one minus y squared. Do you? Why use the foil method to expand. Now we're at the point where we can find the integral use the power method, increase the experiment by one divide by the new exponents. Now we can plug in and we end up with power over three.