Use a Computer Algebra System to Compute the Flux of F

Multiple Choice

Use a computer algebra system to compute the flux of F across S. S is the surface of the cube cut from the first octant by the planes $x = \frac { \pi } { 2 } , y = \frac { \pi } { 2 } , z = \frac { \pi } { 2 }$ $\mathbf { F } ( x , y , z ) = 3 \sin x \cos ^ { 2 } y \mathbf { i } + 3 \sin ^ { 3 } z \cos ^ { 4 } z \mathbf { j } + 3 \sin ^ { 5 } z \cos ^ { 6 } x \mathbf { k }$

A) 3
B) 4
C) $6$
D) 0.67
E) 1