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Trig substitution help

  1. Sep 21, 2007 #1

    [itex] \int \frac{x^2}{\sqrt{9-x^2}} [/itex]

    find the integral using trig sub

    [tex] x= 3 \sin {\phi} [/tex]

    replace 3sin[tex]\phi[/tex] into x and solve. I got to

    \int \frac{9-9 \cos{\phi}}{3 \cos{\phi}}

    then what should I do?
    Last edited: Sep 21, 2007
  2. jcsd
  3. Sep 21, 2007 #2
    Your sub was not correct. When you put in [tex]x=3sin(\Phi) [/tex] you should also write what [tex] d\Phi[/tex] cos now you are integrating over phi and not x anymore. Derivate your sub [tex] x=3sin(\Phi) [/tex] and see what you get. You'll get an integral with [tex] cos^2(\phi) [/tex]. To solve that you shoud see the trig equation for cos(2x) and then it's easy.

    hope it helps
  4. Sep 23, 2007 #3
    I got to [tex] 9 \int \sin^2 \phi [/tex]
    now what?
  5. Sep 23, 2007 #4


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    use [tex]cos2x=1-2sin^2x[/tex]
  6. Sep 24, 2007 #5
    [tex] 9 \int \frac{1 + \cos{2x}}{2} dx [/tex]

    then what
  7. Sep 24, 2007 #6


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    [tex]9\int (\frac{1}{2} + \frac{cos2x}{2} ) dx [/tex]

    Have you ever done Differentiation/Integration of trig functions?
  8. Sep 25, 2007 #7

    Sure I have. Ok thanks for help I got the whole problem cracked!
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