The force F (in newtons) of a hydraulic cylinder in a press is proportional to the square of sec x, where x is the distance (in meters) that the cylinder is extended in its cycle. The domain of F is [0, π/3], and F(0) = 500.

(a) Find F as a function of x.

(b) Find the average force exerted by the press over the
interval [0, π/3].