Integration

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

Integration

Unread post by abir91 » Thu Jan 13, 2011 3:44 pm

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

Have you read the Forum Rules and Guidelines?

Post Reply