Let ${ \vec { F } } = y \vec { i } + x \vec { j }$

Let ${ \vec { F } } = y \vec { i } + x \vec { j }$ .Write down an iterated integral that computes the flux of $\vec { F }$ through S, where S is the part of the cylinder $x ^ { 2 } + y ^ { 2 } = 9$ with x $\ge$ 0, y $\ge$ 0, 0 $\le$ z $\le$ 4, bounded between the planes y = 0 and y = x, oriented outward.

A) $- 2 \int _ { 0 } ^ { 4 } \int _ { 0 } ^ { \pi / 4 } 9 \cos \theta \sin \theta d \theta d z$
B) $2 \int _ { 0 } ^ { 4 } \int _ { 0 } ^ { \pi / 2 } 9 \cos \theta \sin \theta d \theta d z$
C) $2 \int _ { 0 } ^ { 4 } \int _ { 0 } ^ { \pi / 4 } 9 \cos \theta \sin \theta d \theta d z$
D) $- 2 \int _ { 0 } ^ { 4 } \int _ { 0 } ^ { \pi / 4 } 9 \cos \theta \sin \theta d z d \theta$
E) $2 \int _ { 0 } ^ { 4 } \int _ { 0 } ^ { \pi / 4 } 3 \cos \theta \sin \theta d \theta d z$