I'm working on double integrals and am trying to compute the double integral of f(x,y)=x^2 on the region bounded by y=2-x^2 and y=-4.
I first computed this integral as: double of integral of x^2 dy dx. my y limits were y=-4 to y=2-x^2. x limits were x=-6^1/2 to 6^1/2.
I am having problems computing this integral: double integral of x^2dxdy. My x limit is x=sqrt(2-y) to x=0, y limit y=-4 to y=2. I multiplied this by 2 since the length of the x is twice that specified by my integration limits. I do not end up with the correct solution (48* sqrt(6) /5). Anyone know what's wrong with my setup?

Question

I'm working on double integrals and am trying to compute the double integral of f(x,y)=x^2 on the region bounded by y=2-x^2 and y=-4. 
I first computed this integral as: double of integral of x^2 dy dx. my y limits were y=-4 to y=2-x^2. x limits were x=-6^1/2 to 6^1/2.
I am having problems computing this integral: double integral of x^2dxdy. My x limit is x=sqrt(2-y) to x=0, y limit y=-4 to y=2. I multiplied this by 2 since the length of the x is twice that specified by my integration limits. I do not end up with the correct solution (48* sqrt(6) /5). Anyone know what's wrong with my setup?