1. Not finding help here? Sign up for a free 30min 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!

Wierd Integral

  1. Apr 8, 2008 #1
    Why does this work? [​IMG]

    Or maybe a better question is how do you evaluate this integral? Integrate a piecewise function? I tried that an got 0
  2. jcsd
  3. Apr 8, 2008 #2


    User Avatar

    You subtracted when you should've added. It's definitely 2.
  4. Apr 8, 2008 #3
    I get [tex]-e^{-x}, x> 0 -- e^x, x<0[/tex] But I'm unsure as how to go about solving that.

    I evaluated it like this:

    [tex]-e^{-x}|_{x=inf} - e^{x}|_{x=-inf}[/tex] but that's clearly wrong XD
    Last edited: Apr 8, 2008
  5. Apr 8, 2008 #4
    an Improper integral

    you have to Divide the integral in to two
    the first is from -∞ to 0 & the second is from 0 till ∞ and
    HINT: this is an improper integral, consider taking the limit
    for example limC goes to -∞ (of your integral)
    lim D goes to ∞ (of your integral).
    and continue.:smile:
  6. Apr 8, 2008 #5
    [tex]\int_{-\infty}^{\infty}e^{-|t|}dt=\lim_{a\rightarrow -\infty}\int_{a}^{c}e^{-|t|}dt+\lim_{b\rightarrow \infty}\int_{c}^{b}e^{-|t|}dt[/tex]


    [tex] e^{-|t|}=e^{-t}, t>0[/tex] and [tex] e^{t},t<0[/tex]
    YOu can choose c to be any point between negative infinity and positive infinity. Let c=0 so

    [tex]\int_{-\infty}^{\infty}e^{-|t|}dt=\lim_{a\rightarrow -\infty}\int_{a}^{0}e^{t}dt+\lim_{b\rightarrow \infty}\int_{0}^{b}e^{-t}dt[/tex]
  7. Apr 8, 2008 #6
    Yeah I figured it out earlier today. You can do that method or since the function is even throw out the absolute value and evaluate the integral from 0 to infinity and multiply by 2.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Wierd Integral
  1. On Integration (Replies: 4)

  2. An integral (Replies: 2)