# Residue calculus

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

Verify the integral formula with the aid of residues.

1.) Show that the p.v. of the integral of (x^2+1)/(x^4+1) from 0 to infinite =

(pi)/(sqrt 2).

Note: p.v.=principal value; pi is approximately 3.14; sqrt 2=square root of 2

Please show all work and explain the steps, especially how you found the zeros of the function.

Â© BrainMass Inc. brainmass.com December 24, 2021, 5:39 pm ad1c9bdddfhttps://brainmass.com/math/calculus-and-analysis/cauchy-principal-value-residue-60900

#### Solution Preview

Please see the attachment.

Proof:

Since is an even function, then .

Now we compute ...

#### Solution Summary

This shows how to verify an integral formula using residues.

$2.49