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Department of Mathematics

Question

Math 6420 • PDE

Spring 2015 • Question 10

Question

Math 6420 • PDE Spring 2015 • Question 10

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

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

Raw LaTeX

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

\item[(b)]
\[
  I(s)=\int_0^{\pi/2} e^{is\cos x}\,dx
\]
\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