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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

enter image description hereenter image description here

4 Replies
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.

Posted 5 months ago

It has been a while since I've had to do much integration.

If you share the code that you have so far (check out the "How to post..." article), you will likely get some more responses.

Have a great week.

Welcome to Wolfram Community! Please make sure you know the rules: https://wolfr.am/READ-1ST

The 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.

enter image description here

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