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April 19th, 2017, 05:55 PM   #1
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Question How do I solve this integral?

integral ((y - x)^(1/3))/(1 + y + x) dx dy
Integrating over R being a triangle: (0,0) (1,0) (0,1)

I wrote R in the polar form:
0 < theta < pi/4
0 < r < 1/(sin(theta) + cos(theta))

But still can't integrate..
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April 19th, 2017, 06:13 PM   #2
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by examining the symmetry with respect the line $y=x$ it should be pretty clear this integrates to $0$ over that triangle.

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April 20th, 2017, 04:23 AM   #3
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Great!! Well observed!

It can be also solved rotating the coordinate system by pi/4
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