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Crazy integration problem

  1. Sep 29, 2008 #1
    1. The problem statement, all variables and given/known data

    Let [tex]f[/tex] be twice differentiable with [tex]f(0)=6, f(1)=5, [/tex] [tex] f'(1)=2[/tex]
    Evaluate the integral [tex]\int_0^{1}x f''(x) dx[/tex]


    2. Relevant equations

    [tex] \int uv' dx = uv = \int u'v dx [/tex]

    3. The attempt at a solution

    u = x and v' = f''(x)
    so
    u' = 1dx and v = f'(x)
    so

    [tex]xf'(x) - \int_0^{1}f'(x) dx[/tex]

    from here im not sure what to do... maybe parts again...
    u = 1dx and v' = f'(x)
    so
    u' = 0? and v = f(x) //derivative of 1dx is 0 right?
    so

    [tex]xf'(x) - f(x) - \int_0^{1} 0 dx[/tex] ???

    i really dont know. any help would be awesome!!
     
  2. jcsd
  3. Sep 29, 2008 #2

    gabbagabbahey

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    What does the fundamental theorem of calculus say about:

    [tex]\int_0^1 f'(x)dx[/tex]

    ???:wink:
     
  4. Sep 29, 2008 #3
    [tex]\int_0^1 f'(x)dx = f(1) - f(0)[/tex] ??
     
  5. Sep 29, 2008 #4

    gabbagabbahey

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  6. Sep 29, 2008 #5
    wow thats awesome. now i feel retarded haha.
    but seriosuly... thanks gabba!!
     
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