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Substitution of a definite integral

  1. Feb 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Screenshot2012-02-03at14657AM.png

    Why does the 3x^2 disappear? Doesn't it play a role in the answer?
     
  2. jcsd
  3. Feb 3, 2012 #2

    jbunniii

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    It is explained in the first line of blue text:

    [tex]du = 3x^2 dx[/tex]
     
  4. Feb 3, 2012 #3
    I think after you find the derivative of u, which is 3x^2, you divide that by 3x^2 which is 1, but I'm not sure
     
  5. Feb 3, 2012 #4

    jbunniii

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    No, it's a simple substitution.

    [tex]u = x^3 + 1[/tex]

    Differentiating both sides with respect to x:

    [tex]\frac{du}{dx} = 3x^2[/tex]

    or equivalently

    [tex]du = 3x^2 dx[/tex]

    Now substitute into the original integral. The [itex]3x^2 dx[/itex] turns into [itex]du[/itex], and [itex]\sqrt{x^3 + 1}[/itex] becomes [itex]\sqrt{u}[/itex]. The endpoints of the integral also change accordingly.
     
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