Question

Calculate the double integral of f for the corresponding set T as follows:
f(x,y)=x ; T is the limited region by y^(2)=x, y^(2)=2*x, x^(2)=y, x^(2)=2*y.
Method please.

Answer 1

My method is \[\int\limits_{1}^{2}(\int\limits_{\sqrt{x}}^{\sqrt{2x}} x dy)dx - \int\limits_{\sqrt{2}}^{2}(\int\limits_{\sqrt{x}}^{x^2/2} xdy)dx\]

Answer 2

but I don't know if this is correct.