WEBVTT
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So for this problem, we first going to look
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at the region that we have, Um and it's
3
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going to be why equals one half, one minus
4
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X squared. And we're restricting the domain. I'm
5
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from negative one one. So the graph that we
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have on, we're going to, ah, rotate
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this eso we want to look at radius. And
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since they're rotating it around the y axis already,
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this is gonna be why So now what we have
10
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is that the equals Hi, I'm the integral from
11
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negative one toe, one of the radius squared the
12
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radius is gonna be Why so why squared the X
13
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and then we know why is eso we want to
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square Why? And we end up getting, um
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, hi over to we can take out that constant
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and then it's going to be on the inside one
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minus for squared class next to the fourth. We
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can take the integral of this. And what we
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end up getting is ultimately we can do is power
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to, by changing this to zero. So what
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will end up getting if you know, this correctly
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will be for pie over 15. Okay. Um
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and ultimately the best way to get this would be
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through evaluating the integral, um, well, have
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pi over two from 011 minus tease values and plus
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this value evaluated a d. X, and this
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would be our final answer for pi over 15.