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!

Fourier integration help

  1. Oct 14, 2007 #1

    nicksauce

    User Avatar
    Science Advisor
    Homework Helper

    We're doing fourier series in PDEs, and I am left with needing to integrate:

    [tex]\int_0^{\pi}\cos{nx}\sin{x}dx[/tex]

    I completely forget how to integrate this, and I don't have a calculus textbook anymore. Can someone give me a bump in the right direction? I could use maple for the integration, but I would like to know how to integrate it if it came up on an exam.
     
  2. jcsd
  3. Oct 14, 2007 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Convert it into exponentials.
     
  4. Oct 14, 2007 #3

    nicksauce

    User Avatar
    Science Advisor
    Homework Helper

    I have not taken a class in complex vars yet, So I am guessing here. Is this correct?

    [tex]\cos{nx}\sin{x} = Im(e^{inx}e^{ix}) - cos(x)sin(nx)[/tex]
     
  5. Oct 14, 2007 #4

    rock.freak667

    User Avatar
    Homework Helper

    Well I have not done anything on Fourier integration but when I had to do [tex]\int sinNxcosMx dx[/tex]

    You had to use the fact that [tex]sin(A+B)+sin(A-B)=2sinAcosB[/tex]
     
  6. Oct 14, 2007 #5

    nicksauce

    User Avatar
    Science Advisor
    Homework Helper

    Ah, of course.
     
  7. Oct 14, 2007 #6

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If you don't already know the exponential form of the trig functions, then practice deriving trig identities on the spot will probably be more fruitful than trying to memorize (or practice deriving) the exponential forms.

    But, in case you're curious:

    [tex]
    \cos x = \frac{e^{ix} + e^{-ix}}{2}
    [/tex]

    [tex]
    \sin x = \frac{e^{ix} - e^{-ix}}{2i}
    [/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Fourier integration help
  1. Fourier integral help (Replies: 0)

Loading...