# Homework Help: : Integral of (n+1)th derivative

1. Jan 15, 2010

### kfdleb

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)=$$\sum$$ $$\frac{f(r)(a)}{r!}$$(b-a)r +$$\frac{1}{n!}$$ $$\int^{a}_{b}$$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. Jan 15, 2010

### snipez90

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.

3. Jan 15, 2010

### Dick

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.

4. Jan 15, 2010

### kfdleb

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

10x a lot