Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2013 • Question 10

Question

Math 6420 • PDE Fall 2013 • Question 10

Find the leading behavior, as \(s\to +\infty \), of the integral

  1. \[ I=\int _0^3\frac {1}{\sqrt {x^2+2x}}e^{-sx}\,dx, \]
  2. \[ I=\int _0^{\pi /2} e^{is\cos x}\,dx. \]

Raw LaTeX

Find the leading behavior, as \(s\to+\infty\), of the integral
\begin{enumerate}
\item[(a)]
\[
  I=\int_0^3\frac{1}{\sqrt{x^2+2x}}e^{-sx}\,dx,
\]
\item[(b)]
\[
  I=\int_0^{\pi/2} e^{is\cos x}\,dx.
\]
\end{enumerate}

Topic Tags

Cauchy Integral Formula and Integral Theorems Harmonic Functions and Poisson Integral Formula Linear Programming and Optimization Watson's Lemma and Laplace's Method