I have this pdf:

$\displaystyle f(x,y)=\left\{

\begin{array}{lr}

\frac{8}{7}xy&0\le x\le 2;0\le y\le 1; y\le x\\

0&otherwise

\end{array}

\right.$

I want the cdf so I did this:

$\displaystyle F(x,y)=\frac{8}{7}\int\int xy \, dxdy = \frac{2}{7}x^2y^2+C$

I forget how to get rid of C. (0,0) is a point, and (I think) the integral is 0 at this point. Can I just use this to show that C = 0 ?