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Math Help - Integral of Trig function

  1. #1
    Junior Member superman69's Avatar
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    Integral of Trig function

    2∫cos²x dx


    I have trouble solving I tried using u substitution many times and trying to use the identities but I can not some how figure it out. Can someone show me?
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by superman69 View Post
    2∫cos²x dx


    I have trouble solving I tried using u substitution many times and trying to use the identities but I can not some how figure it out. Can someone show me?
    You don't want u-substitution. We have the trig identity: \cos(2x)=2\cos^2(x)-1. Therefore,

    \int2\cos^2(x)\,dx=\int(\cos(2x)+1)\,dx=\frac{1}{2  }\sin(2x)+x+C
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  3. #3
    Junior Member superman69's Avatar
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    I didn't get where the 2 went from 2∫cos²x
    Last edited by superman69; October 21st 2009 at 08:29 PM. Reason: spelling error
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  4. #4
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by superman69 View Post
    I didn't get where the 2 went from 2∫cos²x
    2\int\cos^2x\,dx=\int2\cos^2x\,dx

    It's one of the rules of integrals.
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