Question

Evaluate the following integral using residues: I = { cos(bx)-cos(ax) dx. x2 Let a and b: real constants such that a > b>0. Note: cos(bz)-cos(az) is well-behaved along the real axis (singularity at z = 0 is removable), ejbz-ejaz has a pole at the origin. Make sure to handle this point correctly 22

Answer 1

For this integral, we are using Jordan's lemma , aa theorem and Cauchy residue theorem. These are also mentioned in attached file.
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