Question on Triple Integrals

Posted 5 months ago
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 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?Break/break
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Posted 5 months ago
 Check out this proposed solution on stackexchange. It might give you some ideas.
Posted 5 months ago
 It gave me some ideas, but it didn't quite work. It plotted every point on the object. It didn't give me the x,y, and z boundaries, which are what I'm looking for to set up the triple integral.
 Welcome to Wolfram Community! Please make sure you know the rules: https://wolfr.am/READ-1STThe rules explain how to format your code properly. Images don't help other members to copy your code. Please EDIT your post and make sure code blocks start on a new paragraph and look framed and colored like this. int = Integrate[1/(x^3 - 1), x]; Map[Framed, int, Infinity] You can also embed notebook or attach notebook.