Between the x axis and this semi-ellipse is the base of your wedge. The wedge has a curved wall extending vertically i.e. in the z direction. It also has a flat sloped roof, which has a straight edge that meets all of the straight edge of the base, and which rises from the base at 60 degrees to it, and is semi-elliptical itself, because it disappears where it reaches the vertical elliptical wall.
So you can construct a double or triple integral that totals up a journey going from -2 to 2 or double 0 to 2 in the x direction, stopping at every point to take a detour from 0 to ... in the y direction, and stopping at every point again to take a detour from 0 to ... in the z direction.
Have a go with that?