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

$ \Re_2 $ about $ OC $

$\frac{\pi}{9}$

Applications of Integration

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Missouri State University

Campbell University

Oregon State University

Harvey Mudd College

were given a figure and the figure. A region in a specified line. We have to find the volume generated by rotating this region about this line. The region is. The region are too. Can you rotate about the line formed by Oc? Yeah. An 82 year old. Uh huh. Stickball baseball hat on sq. That way that so looking at the figure, there's three parts. We have the curve. White holds one. You can be up or down. We have blue curve. The curve wife was the fourth root of X. Is a bound on the right and then we have victor's superintendent. The vertical boundary x equals zero on the left group. Now O. C. Is the same as Uh huh. Here, is that the line X equals zero. This is the same as irritating about he Y axis Duke, I'm the Earl of this. And therefore looking at a figure, we get a disc take solid. And so we'll use this method to find the volume. So we want to find the radius right away. It's easy to see that the radius is simply Y equals the fourth root of X. Or instead not 45 X, but three years is X equals Why It's A 4th. And so our volume by the disk method is the equals pi times the integral from Y equals 0 to 1 of our radius wide. The fourth square peg Dy. This isn't easy to grow to evaluate. Once you do, you should get the answer. Hi over nine. That what

Ohio State University

Applications of Integration