Integrate the Function $f$ Over the Surface $S$ Let $S = \{ ( u + v , 3 u + 2 v , 6 v ) : 0 \leq u \leq 1 \text { and } 1 \leq v \leq 3 \}$

Multiple Choice

Integrate the function $f$ over the surface $S$ Let $S = \{ ( u + v , 3 u + 2 v , 6 v ) : 0 \leq u \leq 1 \text { and } 1 \leq v \leq 3 \}$ and $f ( x , y ) = \sin ( x )$

A) $\sin ( 4 ) - \sin ( 3 ) - \sin ( 2 ) + \sin ( 1 )$
B) $19 ( - \sin ( 4 ) + \sin ( 3 ) + \sin ( 2 ) - \sin ( 1 ) )$
C) $- \sin ( 4 ) + \sin ( 3 )$
D) $2 \sqrt { 219 }$