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Iterated Integrals Question, using Tonelli and/or Fubini

  1. Apr 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Let J0(x)=2/[itex]\pi[/itex][itex]\int[/itex]0[itex]\pi[/itex]/2cos(xcos[y])dy. Show that [itex]\int[/itex]0J0(x)e-axdx=[itex]\frac{1}{sqrt(1 +a^2)}[/itex].


    2. Relevant equations
    Tonelli and Fubini's theorems


    3. The attempt at a solution
    Basically I'm finding this problem really hard because I've had to teach myself iterated integrals in order to do it, and I'm not sure if I've learnt the theory correctly! So far I've tried swapping the integrals (using a combination of Tonelli and Fubini's theorems) which means that I'd have to use integration by parts on e^-ax and cos(xcosy) so that doesn't seem to help... I've also tried not swapping the integrals and using substitution (u=xcosy) but that doesn't make it simpler. Any help would be much appreciated!
     
  2. jcsd
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