# Limits for triple integral parabolic cylinder

1,181

## Solution 1

To check the set up we need to make some sketches of the domain as for example in $$z-x$$ and $$z-y$$ planes and also important in the $$x-y$$ plane for $$z$$ fixed that is a rectangular domain from here your set up seems correct.

## Solution 2

Yes, the limits are correct, the volume is given by the following iterated integral $$\int_{z=0}^{4}\left(\int_{x=-\sqrt{z}}^{\sqrt{z}}\left(\int_{y=0}^{4-z} dy\right) dx\right) dz.$$ Can you take it from here? Cartesian coordinates seems to be fine here.

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### Pumpkinpeach

Updated on December 10, 2022

• Pumpkinpeach 11 months

Determine the volume bounded by the parabolic cylinder $$z=x^2$$ and the planes $$y=0$$ and $$y+z=4$$.

My work. I am not sure if I have the correct limits for this question. I used $$x = -\sqrt{z},\dots, \sqrt{z}$$,
$$y= 0,\dots, 4-z$$, $$z=0,\dots,4$$.

It seems too easy, should I be using polars?

• Shaun almost 5 years
Please do not ask questions using pictures of text, since otherwise the question is difficult to search for and some users cannot see the pictures on some devices.
• Robert Z almost 5 years
Fair question! (+1)
• user almost 5 years
If it easy good for you! We don't really need polar in that case since for $z$ fixed the domain is rectangular.
• Pumpkinpeach almost 5 years
I mean its a lot of marks and I felt I hadn't done enough work for it.
• Robert Z almost 5 years
@Pumpkinpeach To avoid downvotes, let us know your progress. BTW please take a few minutes for a tour: math.stackexchange.com/tour
• user almost 5 years
@RobertZ That's a good advice but I don't think that the question posed was totally insufficient. The asker presented his work on that, even if in a short way. Anyway, I agree that the question can be improved adding some more detail abou the result obtained.
• Robert Z almost 5 years
@gimusi I agree, but unfortunately this question got 3 downvotes.
• user almost 5 years
@RobertZ Thise downvotes are not motivated in my opinion, even if I agree that the question can be improved, it doesn't deserve such kind of welcoming.