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August 5th, 2017, 04:29 AM   #1
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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?
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August 5th, 2017, 10:33 AM   #2
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The plane 2x+ 2y+ z= 2 projects to the xy-plane as 2x+ 2y= 2, the line from (1, 0) to (0, 1). That is y= 1- x. To cover the area bounded by the x-axis, the y-axis, 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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