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Math Help - Integral

  1. #1
    Senior Member slevvio's Avatar
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    Integral

    Hello I was wondering if anyone could give me a hand with this.

    Integrate \int\frac{dx}{\sqrt{2x-x^2}}.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by slevvio View Post
    Hello I was wondering if anyone could give me a hand with this.

    Integrate \int\frac{dx}{\sqrt{2x-x^2}}.
    Complete the square in the denominator
    = \int\frac{dx}{\sqrt{1 + -1 + 2x-x^2}}

    = \int \frac{dx}{\sqrt{1 - (x - 1)^2)}}

    Let y = x - 1, so dy = dx
    = \int \frac{dy}{\sqrt{1 - y^2}}

    Does this look familiar?

    -Dan
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  3. #3
    Senior Member slevvio's Avatar
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    thanks!
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  4. #4
    Senior Member slevvio's Avatar
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     \int\frac{dx}{\sqrt{2x-x^2}} = sin^{-1}(x-1) + c ?
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  5. #5
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    Quote Originally Posted by slevvio View Post
     \int\frac{dx}{\sqrt{2x-x^2}} = sin^{-1}(x-1) + c ?
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  6. #6
    Senior Member slevvio's Avatar
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    :d
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