Solution
= Solution
{c}
A <joint probability density function> integrates to one. Here
$$
1=C\int_0^1\int_0^1u(1+2v)\,dv\,du
=C\left(\frac12\right)(2),
$$
so
$$
\boxed{C=1.}
$$
This value also makes the <probability density function> nonnegative everywhere.