What is the Correct Order for Integrating in This Scenario?

[Pearce_09]

Hello,
Consider the integral:
$$\int_R x^2 + y^2 dA$$

with the two graphs 2x-y = 0 and $$x^2$$ - y = 0

therefore y = $$x^2$$ and y = 2x are the two functions
and the point of intersection is at (0,0) and (2,4)

therefore
$$\int { \int x^2 + y^2 dx } dy$$
(a - is top point of the integral and b - is the bottom)

therfor the domain for the first integral (dx) is b = y/2 and a = $$y^1^/^2$$

and for the second integral (dy) is b= 0 and a = 4

but when i switch the order to """"" dy dx... i get a different #.

therefore my new a,b for the integrals are
for the first integral (dy) b = $$x^2$$ a = 2x
for the second integral (dx) b = 0 a = 2

is my change of order correct or did i do somthing wrong??

 

[Pearce_09]

never mind.. my change of order is correct.. i just messed up on my integration
thanks