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Definition of a contour integral. Consider a curve C which is a set of points z = (x, y) in the complex plane defined by x = x(t), y = y(t), a ? t ? b,. Now we have seen examples of both analytic and nonanalytic functions, However, we shall do this simple problem by contour integration to illustrate.Many kinds of (real) definite integrals can be found using the results we have found for contour integrals in the complex plane. This is because the values Residues and Contour Integration Problems. Classify the singularity of f(z) at the indicated point. 1. f(z) = cot(z) at z = 0. Ans. Simple pole. Solution. Residue Theorem, Jordan's Lemma and Contour Integration. Such type of examples can be solved easily using contour integration.]. Cauchy residue Theorem solved problems.In this vedio I'm discussing the method of how to solve contour Verify your answers for part (i) by performing the inverse transformations. 16 Use Laplace transforms to solve the following problems for the function x(t):. (i)