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## Homework Statement

Let R be the rectangle bounded by x - y = 0, x - y = 2, x + y = 0, and x + y = 3. Evaluate

[itex]\int[/itex][itex]\int[/itex](x + y)e

^{x2-y2}dA

R

## The Attempt at a Solution

First I rewrote the boundaries so that I could graph them more easily. I got y = x, y = x - 2, y= -x, and y = -x + 3. I was going to then integrate[itex]\int[/itex](-1≤y≤0)[itex]\int[/itex](-y≤x≤y+2) ((x + y)e

^{x2-y2}) dx dy, and add that to,

[itex]\int[/itex](0≤y≤[itex]\frac{3}{2}[/itex])[itex]\int[/itex](y≤x≤-y+3) ((x + y)e

^{x2-y2}) dx dy

But then I realized I didn't even know how to integrate (x + y)e

^{x2-y2}. This leads me to believe I'm trying to do the wrong thing here. Suggestions?