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!

Homework Help: Need help with simple improper integral

  1. May 20, 2009 #1
    Hey guys, I was doing some homework problems and I ran into a problem regarding how to solve a certain improper integral.

    [tex]\int e^{t*(b-s)}[/tex] evaluated from 0 to [tex]\infty[/tex]

    So I take the integral and get

    [tex]\frac{\int e^{t*(b-s)}}{-(b-s)}[/tex] which evaluated from 0 to [tex]\infty[/tex]

    gives me 0 - [tex]\frac{1}{-(b-s)}[/tex]

    which is 1/(b-s)

    The answer should be 1/(s-b). Can anyone help me figure out what I am messing up?
  2. jcsd
  3. May 20, 2009 #2


    User Avatar
    Homework Helper

    Where does the minus in your second step come from?
  4. May 20, 2009 #3


    User Avatar
    Homework Helper
    Gold Member

    Click on the image below to see how to write this a little nicer with LaTeX:

    [tex]\int_{0}^{\infty} e^{(b-s)t}dt[/tex]

    Is this what you meant? (you didn't actually specify which variable you are integrating over)

    Surely you mean

    [tex]\int_{0}^{\infty} e^{t*(b-s)}dt= \frac{e^{(b-s)t}}{(b-s)} {\left|}_{0}^{\infty}[/tex]


    Also, are you told that [itex](b-s)<0[/itex]? If not, you will need to examine two different cases.
  5. May 20, 2009 #4
    Thanks guys, I feel really stupid now. Earlier today I did a bunch of integrals where the sign on the power was negative and I think I ended up mixing up the what the integral of [tex]e^{at}[/tex] is.

    Also thanks for the tip about Latex
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook