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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6720 • Applied Complex Variables and Asymptotic Methods

Summer 2023 • Question 4

Question

Math 6720 • Applied Complex Variables and Asymptotic Methods Summer 2023 • Question 4

Evaluate the following integral: \[ I=\int _0^\infty \frac {\cos x}{x^2+1}\,dx. \] Clearly indicate the contour of integration and the treatment of the integral along each segment.

Raw LaTeX

Evaluate the following integral:
\[
I=\int_0^\infty \frac{\cos x}{x^2+1}\,dx.
\]
Clearly indicate the contour of integration and the treatment of the integral along each
segment.

Topic Tags

Cauchy Integral Formula and Integral Theorems Contour Integration and Residue Calculus Harmonic Functions and Poisson Integral Formula Real Integral Evaluation by Complex Methods