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Splitting an integral with an absolute value

  1. Mar 12, 2010 #1
    This is a physics problem, but I only need help with the calculus portion of it. I was having trouble figuring out how to split the integral to properly integrate.


    1. The problem statement, all variables and given/known data


    2. Relevant equations

    [tex]\int[/tex][tex]\stackrel{\infty}{-\infty}[/tex](x/x_0)e-2|x|/x_0dx

    where x_o is a constant

    3. The attempt at a solution

    I was wondering how to write the lower part of the integral. What I have is

    [tex]\int[/tex][tex]\stackrel{0}{-\infty}[/tex](x/x_0)e2x/x_0dx+[tex]\int[/tex][tex]\stackrel{\infty}{0}[/tex](x/x_0)e-2x/x_0dx

    Is that right or should I keep the negative in front of the 2 in the lower integral?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 12, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You've got it right. But there is an easy way to do your integral. If f(x) is the integrand, how does f(x) compare with f(-x)?
     
  4. Mar 12, 2010 #3

    Mark44

    Staff: Mentor

    Fixed the LaTeX in your first integral. Double-click it to see what I did.
    Here are some tips:
    Use only a single pair of [ tex] and [ /tex] tags (without the leading spaces that I show) for a given expression. You had tex tags around almost every item.
    Don't mix [ sup] and [ sub] tags inside [ tex] tags. They don't work. Instead use ^{} for superscripts and _{} for subscripts.
     
  5. Mar 12, 2010 #4
    Thanks for the fix. I was struggling with it :P
     
  6. Mar 12, 2010 #5
    I was thinking I could just double the integral from 0 to [tex]\infty[/tex] but because there was an x/x_0 in front and I would have to integrate by parts, I reasoned against it.

    I wouldn't know how else to simplify it.
     
  7. Mar 12, 2010 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yes, if you want to do the integral from 0 to infinity you should integrate by parts. But you can't double it to get the whole integral because the integral from -infinity to 0 isn't the same. How are the two integrals related? You could, of course, just do the integration and find out... But you would be going to a lot of extra work.
     
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