Problem

Refer to the figure and find the volume generated…

04:02

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 $

Answer

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

Discussion

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Video Transcript

it is were given a figure which contains a region and a line can rest to find the volume generated by rotating this region about this line. The region is are one and the line of a rotating about is the line formed by a bee. So looking at the figure, maybe you talk me that way. I you talked me well we rotate the roads hitting about the line. Yes X equals one and therefore what we get is not a washer. Walk here, simply a gift. We're using this method. You laugh. Yeah. One of you. Yeah. Funny. How funny. Right. Crown. So you want to find the radius. Funny how from a figure she had the radius? Yes one minus uh X equals y. Radius is one minus Y. And therefore using the this method the volume is high times the integral from why equals zero. So y equals one of the radius one minus y squared. See why this is a pretty simple integral to evaluate. Once you do, you should get the answer. Hi, over three.

Chris T.

Ohio State University

Topics

Applications of Integration

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 2

Volumes

Problem