Chapter 6.1, Problem 42ES

Use Newton’s Method (Section $4.7$ ), where needed, to approximate the $x\text{-}$ coordinates of the intersections of the curves to at least four decimal places, and then use those approximations to approximate the area of the region.

The region enclosed by the graphs of $y=3-2\cos x$ and $y=2/\left(1+x^2\right)$ .