Can you switch a limit and integral with different variables?

[moo5003]

If you are taking the limit of an integral, can you switch the composition ie: take the integral of a limit if the limit and integral are on separate variables?

Ie:

Lim of z to a [integral over alpha [f(x)/((x-z)(x-a)^2) dx]

=

Integral over alpha[Lim of z to a[f(x)/((x-z)(x-a)^2) dx]

=

Integral over alpha[f(x)/(x-a)^3 dx]

 

[dextercioby]

Since an integration involves limits, and switching the order of taking limits is a tricky business, i'd say that you could do the permutation, as long as there's no infinity (or no indeterminate expression under the limit sign) involved...My guess...

 

[HallsofIvy]

Generally speaking, if both limit and integral are "uniformly convergent" then they can be interchanged.