Problem 39E

Areas of regions

Find the area of the following regions. In each case, graph the relevant functions and show the region in question.

The region bounded by the curve y =10/(x2 − 2x −24), the x-axis, and the lines x =−2and x = 2.

Problem 39E

Solution:-

Step1

Given that

The region bounded by the curve y =, the x-axis, and the lines x =−2 and x = 2.

Step2

To find

Find the area of the following regions. In each case, graph the relevant functions and show the region in question.

Step3

Graph

Step4

Area under the curve

A=dx

=dx

=dx

=

=

=

=[In4-In8]-[In6-In2]

=2In2-3In2-In3-In2+In2

=-(In2+In3) units

Therefore,Area under the curve is -(In2+In3) units