# Thread: Which Contour: Rectangle or Semi-Circle?

1. ## Which Contour: Rectangle or Semi-Circle?

When evaluating a real integral over the real axis (i.e. -infty to + infty) using methods of contour integration, are there any hard and fast rules regarding the integrand which may help in deciding whether to use a Rectangular or a Circular contour, for example?

2. Nobody can help, huh?

3. Originally Posted by Jippo
Nobody can help, huh?
Symmetry is often a good guide.

RonL

4. Originally Posted by Jippo
Rectangular or a Circular contour, for example?
I prefer using a semi-circle.
Because, if you use squares you have,
$\lim_{n\to\infty} \int^n \int^n$
In semi-circles, there is only one variable tending to infinity,
$\lim_{r\to\infty} \int_{-\pi/2}^{\pi/2} \int^r_0$

5. Originally Posted by ThePerfectHacker
I prefer using a semi-circle.
Because, if you use squares you have,
$\lim_{n\to\infty} \int^n \int^n$
In semi-circles, there is only one variable tending to infinity,
$\lim_{r\to\infty} \int_{-\pi/2}^{\pi/2} \int^r_0$
if you have symmetry you can cancel two sides of thesquare.

RonL