Limits and Integrals

  1. 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]
     
  2. jcsd
  3. dextercioby

    dextercioby 12,303
    Science Advisor
    Homework Helper

    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...
     
  4. HallsofIvy

    HallsofIvy 40,308
    Staff Emeritus
    Science Advisor

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