- #1

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## Homework Statement

Integrate exp(-z^2) over the rectangle with vertices at 0, R, R + ia, and ia.## Homework Equations

int(0, inf)(exp(-x^2)) = sqrt(pi/2)

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- Thread starter NT123
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- #1

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int(0, inf)(exp(-x^2)) = sqrt(pi/2)

- #2

ideasrule

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Isn't the contour integral equal to 0 if there are no poles?

- #3

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This is what I would have thought, but I'm supposed to be using the integral of e^(-z^2) to evaluate the real integral int(0,inf)((e^(-x^2))*cos(2ax)), which is apparently equal toIsn't the contour integral equal to 0 if there are no poles?

sqrt(pi)*exp(-a^2)/2.

- #4

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- #5

ideasrule

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If we want to integrate from R+ia to ia, just integrate e^(-z^2)dz=e^-(x+ia)^2 dx from R to 0. Do the same for the other 3 sides. You won't get an analytic answer, but that's OK; just write out the entire contour integral first and you'll see where this is going.

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