Let $\displaystyle f:[0,1]\rightarrow R $be a continuous function such that $\displaystyle \int_{0}^{1}f(x)dx=0$.

Prove that there exists some $\displaystyle c\in(0,1)$ such that $\displaystyle \int_{0}^{c}xf(x)dx=0$

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- Mar 8th 2013, 04:10 PMpankajFind c
Let $\displaystyle f:[0,1]\rightarrow R $be a continuous function such that $\displaystyle \int_{0}^{1}f(x)dx=0$.

Prove that there exists some $\displaystyle c\in(0,1)$ such that $\displaystyle \int_{0}^{c}xf(x)dx=0$ - Mar 8th 2013, 05:05 PMchiroRe: 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?