Find the Work Done by the Force Field $\mathbf { F } ( x , y ) = 2 x y \mathbf { i } + x ^ { 2 } \mathbf { j }$

Multiple Choice

Find the work done by the force field $\mathbf { F } ( x , y ) = 2 x y \mathbf { i } + x ^ { 2 } \mathbf { j }$ on a particle that moves along the curve $\mathbf { r } ( t ) = t ^ { 2 } \mathbf { i } + t ^ { 3 } \mathbf { j } , \quad 1 \leq t \leq 2$ .

A) $127$
B) $128$
C) $63$
D) $64$
E) $31$
F) $32$
G) $15$
H) $16$