La región delimitada por y=x2y = x^2y=x2 e y=2xy = 2xy=2x ∫x=0x=2∫y=x2y=2xdydx o ∫y=0y=4∫x=y/2x=ydxdy\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∫x=0x=2∫y=x2y=2xdydx o ∫y=0y=4∫x=y/2x=ydxdy A=∬D1dxdy=∫x=0x=2∫y=x2y=2xdydx=∫x=0x=2[y∣y=x2y=2x]dx=∫x=0x=2(2x−x2)dx=x2−x33∣02=43A = \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 = \frac43A=∬D1dxdy=∫x=0x=2∫y=x2y=2xdydx=∫x=0x=2[y∣∣y=x2y=2x]dx=∫x=0x=2(2x−x2)dx=x2−3x3∣∣02=34