## Integration

For college and university level advanced Mathematics
abir91
Posts: 52
Joined: Sun Dec 19, 2010 11:48 am

### Integration

Let $f$ be a two times differentiable function on $\mathbb{R}$. Prove that, if $f(0)=f(1)=0$ and $f^{''}$ is continuous on $[0,1]$, then there exists a $c \in [0,1]$ such that,

$\int_{0}^{1} f(x) dx = - \frac{f^{''}(c)}{12}$

If it's too easy for you, try the same problem without the condition, $f^{''}$ is continuous on [0,1].
Abir

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