   Chapter 5.1, Problem 25E

Chapter
Section
Textbook Problem

# Sketch the region enclosed by the given curves and find its area. y = x 4 ,   y = 2 − | x |

To determine

To:

Sketch the region and find the enclosed area.

Explanation

1) Concept:

Formula:

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=x4 and   y=2-x

3) Calculation:

From the graph, the points of intersection are at x=-1 and  x=1. The region is sketched in the following figure.

A=2A1

where A1 is the area under the curve from   x=0 and   x=1

When   x0, 2-|x|=2-x

Here 2-xx4 when   0x1

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