Compute an Exact Integral (AsymptoticIntegrate)

Asymptotic methods can sometimes give exact results for problems because the integrals for the underlying asymptotic series are all zero after a finite number of terms. Here this phenomenon is illustrated with an example from the advanced calculus text by Woods that is mentioned by Richard Feynman in his autobiography.

Use AsymptoticIntegrate to approximate a definite integral.

The higher-order terms do not contribute to the integral.

Hence, the approximation gives the exact value of the integral.