What are the rules for when you can and can not move the limit of a definite integral inside the integration sign?(adsbygoogle = window.adsbygoogle || []).push({});

For example, if I have a definite integral of a function f(z) and the function includes a constant k, and I want to take the limite of the definite integral as k goes somewhere interesting, under what circumstances can I take the limit first of f(z) before interating and get the same answer (if ever)?

Note that this limit has no affect on the limits of integration.

For example:

[tex]

\lim_{r\to\infty} \int_{0}^{2\pi}{e^{r\alpha}e^{ix\alpha} \over 1+e^re^{ix}}dx

[/tex]

for [itex]0<\alpha<1[/itex]

If I can move the limit inside the integral, it is is easy to show that this is 0. Otherwise it is more annoying (and I am pretty the answer here has to be zero).

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Limits of integrals

**Physics Forums | Science Articles, Homework Help, Discussion**