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Homework Statement
Let G be the region bounded by z=x2, z=y2 and z=3. Evaluate :
[itex]\iiint\limits_G |xy| dV[/itex]
Homework Equations
The Attempt at a Solution
So fixing x and y didn't really give me any useful information. When I fixed z though, I got x=±z and y=±z which forms a square in the xy-plane.
So since my function is continuous and I'm integrating over a square, there shouldn't be any issues whether I pick x or y first.
Now I want to get rid of the absolute value, which seems like more of a logical thing than anything else. So since my region is symmetrical over all my quadrants, could I not just take 4 times the integral in the first quadrant thus eliminating the absolute values? That would cover the entire region if I'm not mistaken thanks to symmetry.
So my iterated integral would be :
[itex]4 * [ \int_{0}^{1} \int_{0}^{z} \int_{0}^{z} xy \space dxdydz ][/itex]
Evaluating that would be easy, I'm just hoping I set it up right. If anyone could validate this I would appreciate it very much.
Thanks in advance.
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