Limits and Integrals

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 seperate 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.

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moo5003	Limits and Integrals Tweet 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 seperate 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 Blog Entries: 9 Recognitions: Homework Help Science Advisor	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 Recognitions: Gold Member Science Advisor Staff Emeritus	Generally speaking, if both limit and integral are "uniformly convergent" then they can be interchanged.