Let $f:\mathbb R^2\rightarrow \mathbb R$ be defined by $f(x,y)=cxy$ if $x\geq0 ,y\geq0$ and $x+y\leq1$ and $f(x,y)=0$ otherwise. Find the value of c such that $f$ becomes a probability density function.
If $f$ is a probability density function then integration of $f$ over $\mathbb R^2$ is 1. So I took limit of $x$ between 0 and $1-y$ and took limit of $y$ between 0and 1 and found the integration which gave me $c=24$. Am I correct or did I made some mistake in integration?
Also what will be the marginal density functions?