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Math Help - Can someone help with this integral--I have tried everything I can think of

  1. #1
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    Can someone help with this integral--I have tried everything I can think of

    integral sqrt(18x-x^2) dx

    I completed the square so now I have
    integral sqrt(81-(x-9)^2) dx

    u=x-9
    du=dx

    so now I have integral sqrt(81-u^2) du

    and this is where I get lost. I see that there is a sin in there because 81 is 9^2

    so should it be u=a cos theta?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by operaphantom2003 View Post
    integral sqrt(18x-x^2) dx

    I completed the square so now I have
    integral sqrt(81-(x-9)^2) dx

    u=x-9
    du=dx

    so now I have integral sqrt(81-u^2) du

    and this is where I get lost. I see that there is a sin in there because 81 is 9^2

    so should it be u=a cos theta?
    \int\sqrt{18x-x^2}\,dx=\int\sqrt{81-(x-9)^2}\,dx

    I would recommend the trigonometric substitution x-9=9\sin\theta.

    Can you try it from here?
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