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Math Help - Tricky trig sub integration

  1. #1
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    Tricky trig sub integration

    Hi,

    This is the integral I need to take \int\{x^2}/{\sqrt(9-x^2) \}


    I get to this then dont know what to do \int{x^2}
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  2. #2
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    What substitution did you make?

    Did you try x = 3\sin\theta

    Also remember \displaystyle \sin^2 \theta = \frac{1-\cos \theta}{2}
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  3. #3
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    Hello, highc1157!


    You didn't complete the substitution . . .



    \displaystyle \int \frac{x^2}{\sqrt{9-x^2}}\,dx

    \text{Let: }\:x = 3\sin\theta \quad\Rightarrow\quad dx = 3\cos\theta\,d\theta

    \displaystyle \text{Substitute: }\;\int \frac{\overbrace{9\sin^2\!\theta}^{x^2}}{\underbra  ce{3\cos\theta}_{\sqrt{9-x^2}}}\,\underbrace{(3\cos\theta\,d\theta)}_{dx} \;=\;9\!\1\int \sin^2\theta\,d\theta

    Got it?
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  4. #4
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    yea i get that thanks a lot Sorobon,

    but i'm still having trouble i used the identity for the integral of sine squared and my answer looks nothing like the answer in my book
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  5. #5
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    Quote Originally Posted by highc1157 View Post
    yea i get that thanks a lot Sorobon,

    but i'm still having trouble i used the identity for the integral of sine squared and my answer looks nothing like the answer in my book
    Once you have an answer in terms of \theta you will have to back-substitute x = 3 \sin \theta to get the answer in terms of x. If you need more help, please show all the details of your working (not just one or two steps). I'm sure your classnotes and textbook will have examples to follow ....
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