1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Evaluate this (complicated) integral in two variables

  1. Dec 4, 2008 #1
    1. The problem statement, all variables and given/known data
    I was doing a statistics problem, and ended up with this integral:

    ∫ [1/(2pi)] [e-(w2+z2w2)/2] |w| dw
    How can I evaluate this?

    2. Relevant equations
    3. The attempt at a solution
    1) How can we integrate |w| (with the absolute value)?
    2) What should we do with the z? Can we treat it as a constant here?
    3) Do we need integration by parts here? If so, what should u and dv be? Looks like the thing has no antiderivative...

    Thanks for helping!
  2. jcsd
  3. Dec 4, 2008 #2


    User Avatar
    Science Advisor

    1) Do what you should have learned to do when you first learned about absolute value: break it into "w< 0" and "w> 0". If w< 0, |w|= -w. If w> 0, |w|= w. Do two separate integrals and then add.

    2) Yes, since you are not integrating with respect to z, you are looking for a value for each z and should treat it as a constant as far as the integral with respect to w is concerned.

    3) Looks to me like a simple substitution. Let y= (1+ z)w2.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook