OK, I'm new to multi-variable calculus and I got this question in my exercises that asks me to integrate [itex] e^{-2(x+y)} [/itex] over a diamond that is centered around the origin:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int\int_D e^{-2x-2y} dA[/itex]

where [itex]D=\{ (x,y): |x|+|y| \leq 1 \}[/itex]

I know that the region I'm integrating over is symmetric over the x-axis and the y-axis, but [itex] e^{-x} [/itex] or [itex] e^{-y} [/itex] are neither odd nor even to use the symmetry that way.

Obviously, the diamond is symmetric over the axes [itex] x+y [/itex] and [itex] x-y [/itex]. Does this help?

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# Integrating an exponential function over [itex]|x|+|y| \leq 1[/itex]

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