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: Help with integral

  1. Jan 27, 2013 #1
    This is not a homework problem, but a problem in the textbook that is not required. I am doing this to get a handle on the topic.

    I am evaluating a Fourier transform, without tables, and need to evaluate this integral:

    [tex]
    \int e^{-t} * sin(2 \pi f_c t) * e^{-j2 \pi ft} dt
    [/tex]

    I have tried two methods: 1) integration by parts, and 2) integration after expressing the sine function as a complex exponentials. I get stuck in both cases.

    The asterisks are there to assist with clarity of spacing. Thanks for any help you can provide,
    J
     
  2. jcsd
  3. Jan 27, 2013 #2

    mathman

    User Avatar
    Science Advisor

    Use Euler formula to get exp(-t)*trig function. This is a standard integral (find in table).

    Trig function: sin(at), integral = a/(1 + a2)
    cos(at), integral = 1/(1 + a2)
    (a > 0 for both)
     
  4. Jan 27, 2013 #3
    Thanks, I did try Euler's formula but then worked the integral out manually (attempted to...)

    So this integral I would find in the table exclusively, and never try without a table? The way the drill is stated in the book (not a homework problem.), I wonder if I am to work it out without a table.

    Thanks,
    J
     
  5. Jan 28, 2013 #4

    mathman

    User Avatar
    Science Advisor

    You can integrate by parts twice to get an equation involving the original integral.

    I(exp(-t)cos(at)) = 1 + aI(exp(-t)sin(at)) = 1 - a2I(exp(-t)cos(at))

    Similarly for sin(at) integral.
     
  6. Jan 28, 2013 #5
    Thank you
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook