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: Integral of (n+1)th derivative

  1. Jan 15, 2010 #1
    URGENT: Integral of (n+1)th derivative

    1. The problem statement, all variables and given/known data

    let f(n+1) be integrable on [a;b]; show that

    f(b)=[tex]\sum[/tex] [tex]\frac{f(r)(a)}{r!}[/tex](b-a)r +[tex]\frac{1}{n!}[/tex] [tex]\int^{a}_{b}[/tex]f(n+1)(t)(b-t)ndt

    hint:integrate by parts and use induction

    PLEASE any idea about how to solve it would be really appreciated..... I've been trying for more than an hour but no idea
    Last edited: Jan 15, 2010
  2. jcsd
  3. Jan 15, 2010 #2
    Re: URGENT: Integral of (n+1)th derivative

    Well use the hint. Induct on n. For n = 1, show the equation holds by computing the integral that you get on the RHS after setting n = 1. This is fairly straightforward.
  4. Jan 15, 2010 #3


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    Re: URGENT: Integral of (n+1)th derivative

    Start by actually doing the integration by parts. Treat the integral as u*dv where u=f^(n+1)(t) and dv=(b-t)^n*dt. Once you've got that straight then start worrying about the induction.
  5. Jan 15, 2010 #4
    Re: URGENT: Integral of (n+1)th derivative

    10x a lot
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