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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2019 • Question 9

Question

Math 6420 • PDE Fall 2019 • Question 9

Evaluate \[ I=\int _{-\infty }^{\infty }\frac {\cos (2x)}{(x+1)^2+4}\,dx. \] You must clearly show the contour of integration and treat integration over each contour separately.

Raw LaTeX

Evaluate
\[
  I=\int_{-\infty}^{\infty}\frac{\cos(2x)}{(x+1)^2+4}\,dx.
\]
You must clearly show the contour of integration and treat integration over each contour
separately.

Topic Tags

Contour Integration and Residue Calculus Keyhole and Sector Contours Linear Programming and Optimization Real Integral Evaluation by Complex Methods