August 5th, 2017, 05:29 AM  #1 
Member Joined: May 2017 From: Slovenia Posts: 89 Thanks: 0  Problem with integral bounds
Where P is the part of the plane 2x+2y+z=2 that lies in the first octant. I need to calculate this with Stoke's theorem. I know how to do it but in this case I'm not sure about the bound of the double integral. Any help?

August 5th, 2017, 11:33 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,944 Thanks: 797 
The plane 2x+ 2y+ z= 2 projects to the xyplane as 2x+ 2y= 2, the line from (1, 0) to (0, 1). That is y= 1 x. To cover the area bounded by the xaxis, the yaxis, and y= 1 x, take x from 0 to 1 and, for each x, y from 0 to 1 x. That would be $\displaystyle \int_0^1\int_0^{1 x} dy dx$. 

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