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 \(y=10 /\left(x^{2}-2 x-24\right)\), the x-axis, and the lines x=-2 and 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