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Integrate the following equations using U-Substitution

  1. Feb 3, 2013 #1
    1. The problem statement, all variables and given/known data
    Integrate √(x2(x+3)) from -3 to 0.

    0
    ∫√(x2(x+3)) dx
    -3


    2. The attempt at a solution
    Here is what I did:
    √(x2(x+3))
    = x√(x+3)

    Let u=x+3, du=dx, x=u-3
    Insert the bounds and change the bounds to: 0 to 3.

    x√(x+3)=
    (u-3)√(u)
    = u3/2-3u1/2

    Thus we have:
    3
    ∫(u3/2-3u1/2) du
    0

    Finally:

    (2u5/2)/5-(2u3/2) from 0 to 3.
    Thus I get: -4.15.

    However the correct answer is positive 4.15.
    I know the answer should be positive but what I don't understand is why I'm getting a negative answer. Please help.
    Thanks in advance.
     
  2. jcsd
  3. Feb 3, 2013 #2

    SammyS

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    Gold Member

    Be careful.

    [itex]\displaystyle \sqrt{x^2} = |x|[/itex]

    In fact, for x<0, [itex]\displaystyle\ \sqrt{x^2} = -x\ .[/itex]
     
  4. Feb 3, 2013 #3

    Dick

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    It's positive because if x is negative then sqrt(x^2)=(-x). Right?
     
  5. Feb 3, 2013 #4
    Oh yeah. Silly mistake XD thanks.
     
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