Answer
$3$
Work Step by Step
Stokes' Theorem states that $\iint_{S} curl F \cdot dS=\int_{C} F \cdot dr $
The work done by a force $F$ in moving a particle along path $C$ is: $ \iint_{C} F \cdot dr $
Suppose $S$ to be the part inside the rectangle formed by four points.
We have: $curl F=8 yi+2 z j+2y k$
Now, $\iint_{S} curl F \cdot dS=\iint_{D} 2y-z dA=\dfrac{3}{2} \iint_{D}y dA$
or, $=\dfrac{3}{2} \int_{0}^1 \int_0^2 y dy dx$
or, $=\dfrac{3}{2} \int_{0}^{1} [\dfrac{y^2}{2}]_0^2 dx$
or, $=\dfrac{3}{2} \int_0^1 2 dx$
Now, work done =$\int_{C} F \cdot dr =3$
