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Evaluate using Integration by parts

  1. Sep 15, 2010 #1
    1. The problem statement, all variables and given/known data

    If g(1)=3, g(5)=8 and the integral from 1 to 5 of g(x)dx=-9. Then, evaluate the integral from 1 to 5 of xg'(x)dx.

    2. Relevant equations and attempt at solution

    I used integration by parts to get =xg(x)-(integral of)g(x)dx from 1 to 5. Then substituting in, I get ((5)(8)+9)-((1)(3)+9)=37

    Apparently that answer is incorrect. What am I missing? Thanks.
  2. jcsd
  3. Sep 15, 2010 #2
    You didn't think of the integral in the right way. You are already provided the answer for the complete integral of g(x)dx. You don't need to apply it twice.

    you should get xg(x) from 1 to 5 giving you 40-3=37. Then the integral will give you --9=+9

    Final answer is 37+9=46

    Note: [tex]\int_a^b u\; dv=[uv]_a^b-\int_a^b v\; du [/tex]
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