So I'm learning multivariable calculus and trying to learn Mathematica at the same time. I have a question on triple integrals. Below, I'll post some screenshots from a document I found on the internet. But to ask the question up front: for complex surfaces, how do I get Mathematica to calculate the boundaries for each integral. That is, I can use contourplot to graph the surfaces and then regionplot to see the actual intersection. Doing the integral is easy ONCE I know the boundaries, but how do I get Mathematica to calculate these for me so that I can use the 'integrate' function.
As promised, here is the example. You'll see on the last step, calculating the integral, it doesn't show how the boundaries were found; it just adds them in. Help?
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