Find the Work Done by the Force Field $\mathbf { F } ( x , y ) = x \sin ( y ) \mathbf { i } + y \mathbf { j }$

Multiple Choice

Find the work done by the force field $\mathbf { F } ( x , y ) = x \sin ( y ) \mathbf { i } + y \mathbf { j }$ on a particle that moves along the parabola $y = x ^ { 2 }$ from $( 1,1 )$ to $( 2,4 )$ .

A) $\frac { ( 15 + \sin ( 1 ) - \cos ( 4 ) ) } { 2 }$
B) $\frac { ( 17 + \cos ( 1 ) - \cos ( 4 ) ) } { 2 }$
C) $\frac { ( 15 + \cos ( 1 ) - \cos ( 4 ) ) } { 2 }$
D) $\frac { ( 15 + \sin ( 1 ) - \sin ( 4 ) ) } { 2 }$
E) $\frac { ( 17 - \cos ( 1 ) + \cos ( 4 ) ) } { 2 }$