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).

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# Limits of integrals

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