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Numerade Educator

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Problem 30 Hard Difficulty

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

$ \Re_3 $ about $ BC $

Answer

$\frac{4 \pi}{15}$

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Video Transcript

We're giving a figure with the region and the line and ratifying the volume generated by rotating this region about this line. The region is R. three. We rotated about the vine through B. C. Hearted person. Yeah. Look at these funny faces. I'm doing these cases usually right now you literally say what? Looking at a figure. The region is founded above by wife was the fourth root of X. And below by wyffels. X. And the line through D. C. Is the same as the line of life was one. All right. Was fucking awesome. But it's just came footage. Yes. Looking at the figure by doing this we get a washer type solid. So we usually wash your method. Now the outer radius of the washer. If you look at the figure. Yeah what is equal to think about that Wife was 1- wife was X. And the inner radius It is one Y equals four threat root of X. Rather than like what's be ahead of trends rather than actually have discerning and therefore by the washer method, the volume is pi times a negro from X equals 0 to 1 of the outer radius, one minus X squared minus the inner radius, 1 -4 Root of X Sweater. Yes, this job and this integral is equal to after you follow things out and taking derivatives four Pi over 15.