Math Is Fun Forum

Kent

Member

Registered: 2007-11-22

Posts: 3

Double Integral

Evaluate

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Double Integral

I’d suggest changing to polar co-ordinates. This looks like it might be easier to integrate in polar form.

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: Double Integral

I'm definitely rusty on double integrals, but I think you just evaluate one integral at a time and consider all other variables as constants.  For this problem, use substitution:

This substitution removes that ugly square root from the denominator, but we're left with an extra x.  Solving for x in terms of u gives us

We're now left to evaluate the following integral:

Evaluate the inside integral, pretending that y is a constant.  You should end up with a function in terms of y, which you then integrate over 0 to 1 for the final answer.

Edit: Or use Jane and Krizalid's method, it looks much more clean.

Last edited by TheDude (2007-11-23 04:55:55)

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Wrap it in bacon

Krizalid

Member

Registered: 2007-03-09

Posts: 51

Re: Double Integral

I’d suggest changing to polar co-ordinates.

To do that, split the original square into two triangles: