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Limits and Integrals

by moo5003
Tags: integrals, limits
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moo5003
#1
Feb28-07, 02:50 AM
P: 207
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]
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dextercioby
#2
Feb28-07, 03:19 AM
Sci Advisor
HW Helper
P: 11,948
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
#3
Feb28-07, 11:02 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,682
Generally speaking, if both limit and integral are "uniformly convergent" then they can be interchanged.


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