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1) problem statement: here is the region of the integration of the integral: -1 to 1, x^2 to 1, 0 to 1-y dzdydx. Those bounds go from the outermost integral to the innermost. The problem asks to rewrite the integral as dxdzdy and dzdxdy. I have the 3d drawing of the region as well as the xy, xz, yz plane drawings. I know the drawings are correct, because my professor gave them to me. I'm struggling to see why some of the bounds are what they are. Like, dzdxdy has 0 to 1-y as the bounds for dz, but based on the plane drawings, I don't see why it would not be -sqrt(1-z) to sqrt(1-z). Also, with dxdzdy, the bounds for dx are: -sqrt(y) to sqrt(y), but again I had -sqrt(1-z) to sqrt(1-z). This unit has given me a lot of trouble, so any help is greatly appreciated!

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# Homework Help: Rewrite the integral as an equivalent iterated integral in the order

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