7. Sketch the solid whose volume is given by the iterated...

7. Sketch the solid whose volume is given by the iterated integral given below and use the sketch to rewrite the integral using the indicated order of integration. ??² ??² ??^?(4-y²) dz dx dy Rewrite the integral using the order dz dy dx.

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Transcript

00:01 Okay, so we have zero, oh, sorry, z going from zero to z equals the square root of four minus y squared.

00:12 Okay, i'm going to put a plus sign there, so you remember it means z is the positive square root.

00:17 But if i square both sides, i get z equals, z squared equals four minus y squared, or y squared plus z squared equals four.

00:27 That's a circle in the yz plane of radius 2.

00:31 Oh, sorry, a half circle because it's only the top half.

00:36 Okay, radius 2.

00:37 So this is the yz plane here.

00:44 It's the worst circle ever.

00:46 Let me drag in.

00:47 Oops.

00:52 Okay, and because there's no x in it, what that does is make this like half pipe.

01:03 Okay, it's still not very circular looking, but that's kind of it.

01:09 Okay.

01:10 And x is going from x equals y to x equals two.

01:16 X equals y to x equals y to x equals two.

01:20 So x equals y.

01:22 Now i'm in the x, y plane, which is like the bottom here.

01:29 Okay, now that's flat on the floor of that cylinder thing.

01:38 Okay, that's supposed to be one solid line there, going through at 45 degrees.

01:45 So x is going from y, so that thing out to x equals 2.

01:52 Okay, so let's put that right here.

01:58 X equals 2...

Question

7. Sketch the solid whose volume is given by the iterated integral given below and use the sketch to rewrite the integral using the indicated order of integration. ??² ??² ??^?(4-y²) dz dx dy Rewrite the integral using the order dz dy dx.

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