Suppose that

$$u=y^{2} \sin (x z)+x y^{2} z \cos (x z), \quad v=2 x y \sin (x z), \quad w=x^{2} y^{2} \cos (x z)$$

Show that $u d x+v d y+w d z$ is an exact differential.

Show that

$$\int_{(0,0,0)}^{(\pi / 2,1,1)} u d x+v d y+w d z=\frac{\pi}{2}$$