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Math Help - integral help....?

  1. #1
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    integral help....?

    I tried to understand a solution of an integral here: (the first)
    http://www.mathhelpforum.com/math-he...integrals.html

    why this integral is ZERO ?
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  2. #2
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    Quote Originally Posted by Phoebe83 View Post
    why this integral is ZERO ?

    \int_0^{\pi} \tan^{-1}(\cos(x))dx
    Because the integrand is antisymetric about x=\pi/2.

    RonL
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  3. #3
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    I know that COSX is antisymetric about x=pi/2 but there is tan^-1 there, what about it ?
    (sorry for beeing annoying)
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  4. #4
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    Quote Originally Posted by Phoebe83 View Post
    I know that COSX is antisymetric about x=pi/2 but there is tan^-1 there, what about it ?
    (sorry for beeing annoying)
    Hello Phoebe,

    I've attached a diagram of your function. You'll notice that it is antisymmetric as CaptainBlack stated.
    In the drawing the value of the integral is called a.

    EB
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  5. #5
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    Quote Originally Posted by Phoebe83 View Post
    I know that COSX is antisymetric about x=pi/2 but there is tan^-1 there, what about it ?
    (sorry for beeing annoying)
    cos(x) is anti-symmetric about pi/2, and tan^-1 is antisymnetric about 0,
    which is what we need to conclude that the composite function is anti-
    symmetrix about pi/2, since cos(x) maps pi/2 to 0.

    RonL
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