Answer
$$\eqalign{
& \left( {\text{a}} \right){\text{Graph}} \cr
& \left( {\text{b}} \right){\text{The intersection points are difficult to find by hand}}. \cr
& \left( {\text{c}} \right)A \approx 6.3043 \cr} $$
Work Step by Step
$$\eqalign{
& y = {x^2},{\text{ }}y = 4\cos x \cr
& \cr
& \left( {\text{a}} \right){\text{Graph shown below}} \cr
& \cr
& \left( {\text{b}} \right){\text{From the area shown below we can define the area of}} \cr
& {\text{the region as:}} \cr
& A = \int_{ - a}^a {\left[ {4\cos x - {x^2}} \right]} dx \cr
& {\text{We can see that the antiderivative of the integrand}}{\text{, is easy}} \cr
& {\text{to calculate using the elementary antiderivative}}{\text{, but the}} \cr
& {\text{intersection points }}x,{\text{ it is hard because the equation}} \cr
& 4\cos x = {x^2}{\text{ it is difficult to find by hand}}. \cr
& \cr
& \left( {\text{c}} \right){\text{ From the graphing utility we can approximate the area}} \cr
& A \approx 6.3043{\text{ and with }}a = 1.2015 \cr} $$
