Limits and Integrals

by moo5003
Tags: integrals, limits
moo5003 is offline
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?


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]
Phys.Org News Partner Science news on
Internet co-creator Cerf debunks 'myth' that US runs it
Astronomical forensics uncover planetary disks in Hubble archive
Solar-powered two-seat Sunseeker airplane has progress report
dextercioby is offline
Feb28-07, 03:19 AM
Sci Advisor
HW Helper
P: 11,866
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 is offline
Feb28-07, 11:02 AM
Sci Advisor
PF Gold
P: 38,904
Generally speaking, if both limit and integral are "uniformly convergent" then they can be interchanged.

Register to reply

Related Discussions
Limits, infinity, and cardinality (oh, and integrals too) Calculus 11
couple of integrals questions (and with limits) Calculus & Beyond Homework 3
integrals and limits. Calculus & Beyond Homework 6
limits of integrals Calculus 9
Integrals with no limits. (Backwards differientation) Calculus 3