WEBVTT
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If you wish to draw the diagram for this question
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, you will see that it will look something like
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this giving us a shaded region over here, as
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you can see, which means that we have height
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is four minus y minus princes y squared minus four
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y plus four. Remember, this is because we're
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looking at outer minus inner. And remember, the
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radius is simply why so the height is three.
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Why minus y squared? As I said, the
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radius is why not? Formula for volume is two
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pi times are bound in this case or bounder from
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03 radius times height. Why times three My minus
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y squared radius times height. Pretty straightforward if you
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know what to plug in. Now that we get
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this, let's clean this up a little bit before
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we start integrating. We can simplify this by using
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the distributive property which you London algebra to mean three
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y squared minus y cubed d y. Now that
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we're integrating, we know we're using the power method
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, which means we increase the exponents by one.
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So in this case, the y squared becomes why
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cubed? We divide by the new experiment which in
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this case is actually just gonna be one. Because
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if we divide by three, but we also have
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free on the outside three divided by three is just
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once we actually end up with why cubed? Which
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means we have why cubed minus y to the fourth
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over four. And then this is from 0 to
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3. Now we can plug in zero. Plugged
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in simply yields us zero, which means you don't
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need to worry about that Lower bound. It's just
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the upper bound to be worried about in this problem
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here, you should end up with 27 pi,
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divided by two as your solution.