Explore BrainMass

Explore BrainMass

    Evaluate an improper integral using Jordan's Lemma

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

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Use residues to evaluate this improper integral

    Int(from 0 to inf)[cos(ax)/(x^2+1)]dx (a>0)

    (See attachment for better description.)

    © BrainMass Inc. brainmass.com November 24, 2022, 11:37 am ad1c9bdddf


    Solution Preview

    First, we should determine our contour. We choose the half circle from -R to R.

    So, let's look at what we need to integrate. We need to consider the piece along the x-axis from -R to R, as well as the integral around the half circle. (See attachment)

    So, ...

    Solution Summary

    A step-by-step solution walks the student through the process of evaluating improper integrals using the method of residue. Jordan's Lemma is used in finding the solution. A word file is attached.