Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2020 • Question 9

Question

Math 6420 • PDE Spring 2020 • Question 9

Evaluate \[ I=2\int _{-\infty }^{\infty }\frac {x\sin x}{x^2+4}\,dx. \] You must indicate the contour of integration and treat integration over each contour.

Raw LaTeX

Evaluate
\[
  I=2\int_{-\infty}^{\infty}\frac{x\sin x}{x^2+4}\,dx.
\]
You must indicate the contour of integration and treat integration over each contour.

Topic Tags

Contour Integration and Residue Calculus Fourier Transform and Sampling Theory Linear Programming and Optimization Real Integral Evaluation by Complex Methods