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Integral Help: Completing the square?

  1. Feb 12, 2008 #1
    1. The problem statement, all variables and given/known data

    [tex]\int^{3}_{0}\frac{x^{2}}{(25-4x^{2})^{\frac{3}{2}}} dx[/tex]

    2. Relevant equations



    3. The attempt at a solution

    Not sure on where to start. We learned in class how to complete the square, but i'm not sure if that's what I am supposed to use on this problem. Can anybody give me a hint on where to start? it would be greatly appreciated.

    Thanks,
    Nick
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Feb 12, 2008
  2. jcsd
  3. Feb 12, 2008 #2

    Gib Z

    User Avatar
    Homework Helper

    Here I would use a trig substitution. Also, you forgot the "dx" term. It is very important.

    We have;

    [tex]\int^3_0 \frac{x^2}{ ( 5^2 - (2x)^2)^{3/2}} dx[/tex]

    Can you think of a trig substitution that would make that denominator simpler?
     
  4. Feb 12, 2008 #3
    Oh yea whoops, hmm. [tex]x= asin\theta[/tex]? I'll give it a shot and see what happens. Thanks!
     
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