How do you Evaluate the integral by changing to cylindrical coordinates?
#\int_(-2)^2 \int_(-\sqrt(4-y^(2)))^(\sqrt(4-y^(2)))int_(sqrt(x^2+y^2))^2 (xz) dzdxdy#
The limit on the innermost integral defines the volume inside the cone, vertex at origin, concentric with z-axis, radius 2 at
The other limits lie on or outside this cone and so they can be simplified as follows in cylindrical:
- Note that for every positive
#xz#isnside the cone, there is a corresponding negative #xz#value, so one would expect the integration to result in zero.