a r.v. X is uniformily distributed between [-2,2], and Y=X2
What is the cov(X,Y)?
Note that for X ~ U(-2, 2) the pdf of X is $\displaystyle f(x) = \frac{1}{4}$ for $\displaystyle -2 \leq x \leq 2$ and zero elsewhere.
$\displaystyle Cov(X, Y) = E(XY) - E(X) E(Y) = E(X^3) - E(X) E(X^2)$.
Definition: $\displaystyle E(X^n) = \int_{-\infty} ^{+\infty} x^n f(x) \, dx$.
The calculus is left for you to do.