Total mass of region R

Question

in this question how can I arrange the boundarys, I mean how can i do parametrization ?

Region: $R$ which lies between the function $y=x^2$ and $y=2(2x)^{0.5}$ Density of the region: $f(x,y)=(x^2+y)^{0.5}-2y $

what is the total mass of the region $R$ ?

Answer 1

Hint:

$y=x^2$ and $y=2(2x)^{0.5}$ for $x \in\{0,2\}$

Answer 2

Hint:

$$\int_0^2\int_{x^2}^{2\sqrt{2x}}f(x,y)dydx = \int_0^4\int_{\frac{y^2}4}^{\sqrt y}f(x,y)dxdy$$