Evaluate the Surface Integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$

Short Answer

Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ for the vector field $\mathbf { F } ( x , y , z ) = - x \mathbf { i } - y \mathbf { j } + z ^ { 2 } \mathbf { k }$ where S is part of the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ between the planes z = 1 and z = 2 with upward orientation.