Basic Trig Integral Question.

  1. 1. The problem statement, all variables and given/known data
    This question is part of Fourier Series in Circuit Analysis. There were fairly straightforward integrals which I calculated and confirmed using MAPLE to be correct, however the book gives somewhat different answers. I would presume that what I did was correct and the solutions manual made an error, however since it's a fairly large question with answers being carried forward I want to make doubly sure. Sorry about the size of the images, I will remove them after the problem

    This is the integral essentially, the definite integral from 2 to 4 is left out because it's zero,

    f(t) = 5 for 0 < t < 1
    f(t) = 10 for 1 < t < 2


    2. Relevant equations

    cos (Pi/2) = (-1)[itex]^{\frac{n-1}{2}}[/itex]

    cos (Pi) = (-1)[itex]^{n}[/itex]

    3. The attempt at a solution

    My answer came to this:


    EDIT: cos(nPi/2) goes to (-1)^n/2 - still doesn't reconcile my answers with the book though.

    The MAPLE output was:

    [itex]5\,{\frac {1+\cos \left( 1/2\,n\pi \right) -2\,\cos \left( n\pi
    \right) }{n\pi }}[/itex]

    The answer in the book was (last line before the table):


    As you can imagine, because the answers are different, the values in the table are going to be different and hence whatever I have to plot afterwards will be different.
    Last edited: Apr 9, 2012
  2. jcsd
  3. gneill

    Staff: Mentor

    ##(-1)^{integer}## cannot produce any zeros, it can only produce +1 or -1. So it doesn't replace ##cos(n \pi / 2)##.
  4. I should have been clearer, cos (n*Pi/2) is replaced by (-1)^n/2

    So if n = 3, I'm guessing that term is ignored because you can't compute that. At least that's the identity they gave in the book.
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