Chapter 5.4, Problem 57E

(a)

To determine

To calculate: Force $F$ as a function of $x$ given force is proportional to square of $\sec x$ and domain of $F\left(x\right)$ is $\left[0,\frac{\pi }{3}\right]$ and $F\left(0\right)=500$.

(b)

To determine

To calculate: Average value of a function $F\left(x\right)=500{\sec }^{2}x$ over the given interval $\left[0,\frac{\pi }{3}\right]$