   Chapter 5.1, Problem 40E

Chapter
Section
Textbook Problem

# Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves. y = x − cos x ,   y = 2 − x 2

To determine

To find:

Approximate x-coordinates of the points of intersection of the given curves, and find the area of the region bounded by the curves.

Explanation

1) Concept:

The area A of the region bounded by the curves y=f(x), y=g(x) and the lines x=a and x=b is

A= abfx-gxdx

fx-gx=fx-gx when fxg(x)gx-fx when gxf(x)

2) Given:

y=x-cosx,   y=2-x2

3) Calculation:

fx=x-cosx and gx=2-x2

i) To find the intersection points of the curves draw the graph.

From the sketch, it is clear that the curves intersect at x-1.189, x1.135

In the interval -1.189, 1.135

ii) the upper curve is y=2-x2 and the lower curve is y=x-cosx

A=-1

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