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Math Help - integration

  1. #1
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    integration

    Can someone please help me integrate 1 - (cos x)^2 ?
    Thanks!
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  2. #2
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    Quote Originally Posted by turtle View Post
    Can someone please help me integrate 1 - (cos x)^2 ?
    Thanks!
    You can write,
    \int (1+\cos x)(1-\cos x) dx
    By difference of two squares.
    Now, use integration by parts.
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  3. #3
    Junior Member AlvinCY's Avatar
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    There's nothing wrong with what TPH is doing :-),

    I personally hate integration by parts. It's long and dreaful, personally:

    \int 1 - cos^2 x\,dx
    =\int sin^2 x\,dx, using double angle formula for cos2x,
    =\int \frac{1 - cos2x}{2}\,dx
    =\int \frac{1}{2} - \frac{cos2x}{2}\,dx
    =\frac{x}{2} - \frac{sin2x}{4} + C

    Tada!
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