April 19th, 2017, 05:55 PM  #1 
Newbie Joined: Apr 2017 From: Brazil Posts: 5 Thanks: 0  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.. 
April 19th, 2017, 06:13 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,930 Thanks: 998 
by examining the symmetry with respect the line $y=x$ it should be pretty clear this integrates to $0$ over that triangle. 
April 20th, 2017, 04:23 AM  #3 
Newbie Joined: Apr 2017 From: Brazil Posts: 5 Thanks: 0 
Great!! Well observed! It can be also solved rotating the coordinate system by pi/4 

Tags 
integral, polar, solve 
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