Question

Evaluate the triple integral (1+z^2)dV over D, where D is the solid region bounded below by the upper portion of the cone z^2=3x^2+3y^2 and above by the sphere x^2+y^2+z^2=4

Answer 1

z would go from

\[\int _{\sqrt{3 x^2+3 y^2}}^{-\sqrt{-x^2-y^2+4}}\]

Answer 2

so should i integrate z with those limits and then change to polar coordinates?