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March 26th, 2014, 12:40 AM   #1
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Triple integral

Hi. Now i learning. I solve almost all examples from my book, but thease two remain, there are to hard to solve them. Can someone to show the solution ?
Thanks


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March 26th, 2014, 06:20 AM   #2
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Re: Triple integral

First, these are not "triple" integrals. They are just double integrals.

Quote:
Originally Posted by Math_user
Hi. Now i learning. I solve almost all examples from my book, but thease two remain, there are to hard to solve them. Can someone to show the solution ?
Thanks

You are integrating over the unit disk and the integral involves "" so changing to polar coordinate looks simplest. In polar coordinates, r goes from 0 to 1 while goes from 0 to . Of course, becomes . The integral becomes

The substitution seems obvious.

Quote:
Here the integration is over the ellipse. The substitution, , , a variation on polar coordinates looks like it should work. That way the boundary of the
region is , the circle with radius 1. The integral becomes
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March 26th, 2014, 08:13 AM   #3
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Re: Triple integral

The OP's question states that rather than which suggests that is constant and we thus have a single integal with respect to . Similarly for the second example.
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March 26th, 2014, 01:40 PM   #4
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Re: Triple integral

Thanks, you are awesome.
P.S. Yes, i know there are double, just little bit confusing until i try to look in book and to write here.
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March 27th, 2014, 06:18 AM   #5
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Re: Triple integral

Quote:
Originally Posted by v8archie
The OP's question states that rather than which suggests that is constant and we thus have a single integal with respect to . Similarly for the second example.
I suspect that the "=" was an error since then the double integral would be 0.
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