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