La región delimitada por $y = x^2$ e $y = 2x$ $$\int_{x=0}^{x=2}\int_{y=x^2}^{y=2x}dydx\;\;\;\text{ o }\;\;\;\int_{y=0}^{y=4}\int_{x=y/2}^{x=\sqrt{y}}dxdy$$ $$A = \iint_D1dxdy = \int_{x=0}^{x=2}\int_{y=x^2}^{y=2x}dydx = \int_{x=0}^{x=2}\bigg[y\bigg|_{y=x^2}^{y=2x}\bigg]dx = \int_{x=0}^{x=2}(2x-x^2)dx = x^2-\frac{x^3}{3}\bigg|_0^2 = \frac43$$