# Residual calculus

Not what you're looking for? Search our solutions OR ask your own Custom question.

Use residue theory to compute the integral:

Use residue theory to compute the integral:

I know that the singular points are 4i and -4i, and that I need to integrate from -R to R and then around the half circle from 0 to pi. Only 4i is in this half-circle, so I need to calculate the residue for 4i. This is where I get stuck and then I need to know how to put it all together at the end. Please advise, and show each step. Thanks!

Â© BrainMass Inc. brainmass.com November 24, 2022, 11:54 am ad1c9bdddfhttps://brainmass.com/math/calculus-and-analysis/computing-integral-using-residues-29314

#### Solution Preview

Please see the attachment.

Let's consider the integral , where and is consist of the half circle and the line segment from ...

#### Solution Summary

This shows how to use residue theory to compute the integral. The expert calculates the residues for half-circles.

$2.49