Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2017 • Question 9

Question

Math 6420 • PDE Fall 2017 • Question 9

Evaluate the integral \[ \int _0^\infty \frac {\sin (ax)}{x}\,dx \qquad \text {for }a>0. \] You must clearly show the contours of integration and treat integration over each contour separately.

Raw LaTeX

Evaluate the integral
\[
  \int_0^\infty \frac{\sin(ax)}{x}\,dx
  \qquad\text{for }a>0.
\]
You must clearly show the contours of integration and treat integration over each contour
separately.

Topic Tags

Cauchy Integral Formula and Integral Theorems Contour Integration and Residue Calculus Linear Programming and Optimization Real Integral Evaluation by Complex Methods