$B=\{(x,y,z) \in\mathbb R^3| \; x^2+y^2+4z^2 \le3, \;x^2-y^2+4z^2\le1, \; z\ge 0\}$
The question is similar to that which I shared in another topic. Also here, the set is defined by an ellipsoid, an elliptic hyiperboloid and by the positive half-space of z.
Therefore, I relize that I have to solve $\iiint_B1 \;dxdydz$ after studing or changing the equations correctly. Are the cylindrical coordinates useful for the solution? Is it the only way?
I trust in you!