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Missing something simple

  1. Jan 30, 2008 #1
    Hi everyone,
    I know I am missing something simple from this integration.

    integrate from l to -l

    [tex]\int[/tex]cos ((k*pi*x)/l) * cos ((k*pi*x)/l)dx

    I use the identity cos u cos v = 1/2 [cos(u-v) + cos(u+v)]

    which gives me the following to integrate from l to -l

    1/2[cos (2k*pi*x)/l]dx

    I bring 1/2 out of integration

    so when i integrate [cos (2k*pi*x)/l]dx

    i get [sin (2k*pi*x)/l] / [(2k*pi)/l]

    now i move the numerator out so the outside becomes l/4*k*pi
    and the inside is [sin 2*k*pi + sin 2*k*pi]

    Now my problem is this sin 2 k pi is zero
    hence if i multiply it by the outside it will become zero but the answer is l

    I know I am missing a simple step but dont know where.

    Thanks guys
     
  2. jcsd
  3. Jan 30, 2008 #2
    You are just overlooking the fact that cos(0)=1, not 0.
     
  4. Jan 30, 2008 #3
    i am sorry i didnt get you there. I know cos 0 is 1 but I am using sin at the very end which is zero if sin 2*k*pi
     
  5. Jan 30, 2008 #4
    Well what happened to the cos(u-v) term in your identity?
     
  6. Jan 30, 2008 #5
    Oh! I didnt see that one. Silly Silly mistake. Thanks dhris
     
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