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Substitution of a definite integral

  1. Feb 4, 2012 #1
    1. The problem statement, all variables and given/known data

    Screenshot2012-02-04at91000PM.png

    Screenshot2012-02-04at90922PM.png

    3. The attempt at a solution

    I don't see why the √v disappears in this step

    Screenshot2012-02-04at91249PM.png

    I understand how they got the 20/3, because they integrated, but if they're integrating then I would think v^-1/2 would become (v^1/2)/(1/2)
     
    Last edited: Feb 4, 2012
  2. jcsd
  3. Feb 4, 2012 #2

    Curious3141

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    Homework Helper

    The √v disappears because [itex]dv = \frac{2}{3}v^{-\frac{1}{2}}du[/itex] (rearranging the equation they gave for du). Substitute that for dv into the integrand and you'll see why. The 20/3 comes from 10*(2/3) during this substitution, NOT from integration (which hasn't occurred yet).
     
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