# Find c

• March 8th 2013, 04:10 PM
pankaj
Find c
Let $f:[0,1]\rightarrow R$be a continuous function such that $\int_{0}^{1}f(x)dx=0$.

Prove that there exists some $c\in(0,1)$ such that $\int_{0}^{c}xf(x)dx=0$
• March 8th 2013, 05:05 PM
chiro
Re: Find c
Hey pankaj.

Can you split the integral up into pieces where f(x) <= 0 and f(x) > 0 and show that some c exists to balance the first integral?