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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1996 • Question 8

Question

Math 6420 • PDE Fall 1996 • Question 8
Compute the following integral. Use the Jordan lemma. \[ \int_0^\infty \frac{x\sin x}{x^2+1}\,dx. \] **Applied Math Qualifying Exam Part C** Do two out of the four problems for full credit on Part C.

Raw LaTeX

Compute the following integral. Use the Jordan lemma.
\begin{equation}
  \int_0^\infty \frac{x\sin x}{x^2+1}\,dx.
\end{equation}
\end{enumerate}

\examheading{Applied Math Qualifying Exam Part C}

Do two out of the four problems for full credit on Part C.

\begin{enumerate}

Topic Tags

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