Evaluate $\iint _ { S } \frac { x ^ { 2 } + z } { x ^ { 2 } + y ^ { 2 } } d S$

Short Answer

Evaluate $\iint _ { S } \frac { x ^ { 2 } + z } { x ^ { 2 } + y ^ { 2 } } d S$ , where S is the part of the surface $z = x y$ that lies between the cylinders $x ^ { 2 } + y ^ { 2 } = 1$ and $x ^ { 2 } + y ^ { 2 } = 4$ .