   Chapter 7.R, Problem 74E

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# Find the area of the region bounded by the curves y = 1 / ( 2 + x ) , y = 1 / ( 2 − x ) , and x = 1 .

To determine

To find:

The area bounded by the two curves.

Explanation

Given:

The two curves are y=12+x, y=12x and x=1

Formulae used:

The simple integration.

Consider y=12+x, y=12x and x=1

Hence, use the method of simple integration

Graph of the curves are

From the graph, limits of integration will be from 0 to 1

Therefore, the area becomes

A=01(12x12+x)dxt=xdt=12xdx2tdt=dx

Simplify and get:

A=01(12x12+x)dx=01(12t12+t)2tdt=

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