Answer
See the explanation
Work Step by Step
The two curves intersect in:
$$\sqrt x=x^2$$ $$x^4-x=0$$ $$x(x-1)(x^2+x+1)=0$$ $$x_1=0,x_2=1$$
a) We have:
$$\begin{aligned}
\int\int_R f(x,y)dA&=\int_0^1\int_{x^2}^{\sqrt x} f(x,y)dydx.
\end{aligned}$$
b) $$\begin{aligned}
\int\int_R f(x,y)dA&=\int_0^1\int_{y^2}^{\sqrt y} f(x,y)dxdy.
\end{aligned}$$
