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Definite Integration

  1. Feb 12, 2012 #1
    1. The problem statement, all variables and given/known data

    Integrate x^2(x+1)^1/2 for x=0 x=3

    2. Relevant equations



    3. The attempt at a solution

    I start with substitution u=x+1
    and du=dx

    I have no clue where to go from here. How do I take care of that x^2?

    This looks like it would be simple but it's giving me a hell of a time.

    Jim
     
  2. jcsd
  3. Feb 12, 2012 #2
    Try integration by parts.
     
  4. Feb 12, 2012 #3

    SammyS

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    That substitution, u=x+1, should work fine, and allow you to complete the integration.

    What do you get for the integrand when you use that substitution?
     
  5. Feb 13, 2012 #4
    Looking through my textbook I realized that we already solved this one as an indefinite integral... kind of embarrassing.

    Dealing with the x^2 was the hardest, but the integrand is:

    u=x+1
    du=dx
    x^2=(u-1)^2 <---- Much easier looking at it now.

    ∫(u-1)^2u^1/2du

    Thanks for the help as always!
     
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