Answer
$0$
Work Step by Step
Here, we have
As we know that $\dfrac{\partial f_2}{\partial x}=8y siny$
and $\dfrac{\partial f_1}{\partial y}=8x cos y$
Thus, $\oint_C F \cdot dr=\iint_S (\dfrac{\partial f_2}{\partial x}-\dfrac{\partial f_1}{\partial x}) dA$
$\int_{0}^{\pi/2}\int_{0}^{\pi/2} (8y siny-8x cos y) dy dx=\int_{0}^{\pi/2} (\pi^2 \sin x -8x) dx$
This implies that
$(\pi^2 \cos x -4x^2)_{0}^{\pi/2}=0$
