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Integral of a continuously differentiable function on [a,b].

  1. Jan 13, 2008 #1
    suppose f is real, continuously differentiable function on [a,b], f(a)=f(b)=0 and

    integral f^2dx=1

    show [integral(xf(x)f'(x)dx)= -1/2 over [a,b]
    Last edited: Jan 13, 2008
  2. jcsd
  3. Jan 13, 2008 #2
    How can you write the term [tex]f(x)\,f'(x)[/tex]?
  4. Jan 13, 2008 #3


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    Integrate by parts:

    You will get 1/2(bf2(b)-af2(a)-integral(a,b)f2(x))
  5. Jan 14, 2008 #4


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    Elaborating on Rainbow Child's suggestion, what is the derivative of (f(x))2?
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