If $\vec { F } = 3 x ^ { 2 } \vec { i } + 4 z \sin ( 4 y z ) \vec { j } + 4 y \sin ( 4 y z ) \vec { k }$

Short Answer

If $\vec { F } = 3 x ^ { 2 } \vec { i } + 4 z \sin ( 4 y z ) \vec { j } + 4 y \sin ( 4 y z ) \vec { k }$ , compute $\int_{C} \vec{F} \cdot d \vec{r}$ where C is the curve from A(0, 0, 3)to B(2, 1, 5)shown below.
Hint: messy computation can be avoided.