Find volume of $A=\{(x,y,z): 4x^2+y^2<4,x>0,x^2>z>0\}$. Review solution.

Question

I need to find volume of $A=\{(x,y,z): 4x^2+y^2<4,x>0,x^2>z>0\}$ So we need to count following integral: $\int\int\int_A1dxdyzdz$

First, we see that $x<1$ because $4x^2+y^2<4$.

So $\int_0^1\int_0^{x^2}\int_0^{4-4x^2}1dydzdx=\int_0^1\int_0^{x^2}(4-4x^2)dzdx=\int_0^14x^2(x^2-1)dx$

Is it correct?