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 $\displaystyle \int_{0}^{c}xf(x)dx=0$
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 $\displaystyle \int_{0}^{c}xf(x)dx=0$