Integrable function Please help me prove this.
Suppose $f$ is defined in$\left [ a,b \right ]$ ,$f\geq 0$, $f$ is integrable in$ [a,b]$ and $\displaystyle\int_{a}^{b}fdx=0$
prove:
$\displaystyle\int_{a}^{b}f(x)^2dx=0$  
Thanks a lot!

My first inclination would be to say that since $f\geq0$ and $\int_a^bfdx=0$, $f(x)=0$ for $x$ such that $a\leq x\leq b$.  Because of this, $\int_b^af(x)^2dx=0$.  You will probably need to fill in a fair amount of reasoning to make this hold up, though.  
Also, suggestion - accept some answers to your questions.  It makes people more likely to answer in the future.
