Let $\mathbf { F } ( x , y , z ) = ( x + y ) \mathbf { i } + y \mathbf { j } + z \mathbf { k }$

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = ( x + y ) \mathbf { i } + y \mathbf { j } + z \mathbf { k }$ and S is $z = 1 - x ^ { 2 } - y ^ { 2 }$ between $z = 1 - x ^ { 2 } - y ^ { 2 }$ and $z = 1$ Then the flux of $\text { F }$ through S is

A) $\frac { 3 \pi } { 8 }$
B) $\frac { 3 \pi } { 7 }$
C) $\frac { 3 \pi } { 5 }$
D) $\frac { 3 \pi } { 4 }$
E) $\frac { 3 \pi } { 2 }$