Solución

La región delimitada por y=x2y = x^2 e y=2xy = 2x
x=0x=2y=x2y=2xdydx       o       y=0y=4x=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 A=D1dxdy=x=0x=2y=x2y=2xdydx=x=0x=2[yy=x2y=2x]dx=x=0x=2(2xx2)dx=x2x3302=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 = \frac43