What parametrization should I use for this double integral?

Question

I have this domain: $$D = \{ (x,y) | y \ge0, y \le x\le 1\}, f = \sqrt{4x^2-y^2}$$ I need to evaluate the double integral on this domain. I tried using cartesian coordinates, but after computing the first integral I got a too diffcult one which I couldn't solve.

BTW, in cartesian coordinates I used $0 \le y \le 1$ and $ y \le x \le 1$. Can I use polar coordinates. If so, how? Thanks for your answer!!

Answer 1

Hint: Try integrating over $y$ first.

Answer 2

Hint: Use substitution \begin{align} u &= 2x - y, \\ v& = 2x + y. \end{align}