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mhm. Okay. This integral represents a volume and
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because of the way it's written, you can tell
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that it's big. R squared minus little r squared
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mm So this is a washer. All right.
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So um and since it's dy we're going around the
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y axis and we got a washer. Okay,
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so big are is from here to here. So
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big are is big. R squared is y to
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the fourth. So big are is y squared.
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Okay. But really it's X on the right is
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what I'm going to call it X on the right
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, which is why squared? So why is the
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square root of X? Okay. And then little
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R is the distance from here to here And we
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have little r squared equals coach. Should be white
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to the 8th Equals Way to the 8th. So
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little are is white the 4th and that's X.
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On the left. So to draw that we draw
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wife was The 4th Root of X. Okay.
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And then why is going from 0 to 1?
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Okay, so This is 0-1. So um We
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know it goes through 00 and 11. They both
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do. Okay, so I picked another point that
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I knew both the square root and the fourth root
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of 16. What? 1/16? So the square
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root of 1 16th? It's 1 4th But the
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4th root of 1/16 is 1/2. Okay, so
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that puts The 4th root up on the top because
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a half is more than 1/4. So this is
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the fourth root of X. And then here's the
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square root of X. And then we cut slices
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in it this way and sent them around. Okay
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? So yeah, its shape is like a little
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funnel looking thing, okay, with the outer edge
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being like was the square root of X. And
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the whole in there being like was the 4th root
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of X and it's 0 to 1 and it's rotated
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around the Y axis.