- #1

CAF123

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## Homework Statement

Evaluate the integral by closing a contour in the complex plane $$\int_{-\infty}^{\infty} dx e^{iax^2/2}$$

## Homework Equations

Residue theorem

## The Attempt at a Solution

My initial choice of contour was a semicircle of radius R and a line segment from -R to R. In the limit R to infinity, I would hopefully recover the integral in OP. But then I realized this was going to work because the integral over the semicircle would not vanish when R tended to infinity. My question is, what is the best way to see what the best contour should be for a given problem and how to determine the one right for this problem?

Many thanks