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Odd and even functions

  1. Oct 25, 2004 #1
    f(t) = 1 if -pi/2 <=t <=0
    -1 if 0<=t<= pi/2
    0 elsewhere

    how does integral of f(t)*cost dt become and odd function with the integral limit from - pi/2 to pi/2 ?

    thanks a lot
  2. jcsd
  3. Oct 25, 2004 #2

    Tom Mattson

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    Gold Member

    It's not the integral of f(t)cos(t) that is odd (in fact it's just a number). It's the function f(t)cos(t) itself that is odd.

    Let's see why.

    Let y(t)=f(t)cos(t)
    so, y(-t)=f(-t)cos(-t)

    Note that f(-t)=-f(t) and cos(-t)=cos(t). So,


    and thus y(t) is odd. In general, the product of any even function and any odd function is odd.
  4. Oct 25, 2004 #3
    thanks a lot
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