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Numerade Educator

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Problem 29 Hard Difficulty

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

$ \Re_3 $ about $ AB $

Answer

$\frac{17}{45} \pi$

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Video Transcript

trying to be were given a figure which contains a region in the line And rest to find the volume generated by rotating this region about this line. The region is R. three and we rotated about the line through a. D. It's funny to watch, it's Looking at the figure. It's founded above. By the line. Like was a curb bike was the 4th root of X. Below. By the curve, Y equals X. And the line through A. B. Is the same as the line stand. Who got some X equals Y. You should just they should bring back our this is what did he like just for laughs or something. Problem. Notice that a routine about this line. You appear to get a washer type solid. So we'll use the washer method now redefined the outside radius or outer radius. That's what they fucking girls. So tell a company that this is equal to X equals one minus X equals Y. To the fourth. And the inner radius is one minus X equals Y. Like they all get the fuck. And by the washing method are volume B is pi times the integral from Y equals 0 to 1 of the outer radius, one minus Y to the fourth squared minus one minus Y in a radius square. Do you know why? Yeah, you? Re right. was literally just that I would say 20 after you evaluate this integral, you should get 17 pi over 45 addition. Okay, well I'm gonna stand up comedian.