Using the integral of sec3 u By reduction formula 4 in Section 7.2.

Graph the following functions and find the area under the curve on the given interval.

f(x) = (9 – x2)–2,

Problem 63E

Solution:-

Step1

Given that

f(x)= [0,

=

Step2

To find

Graph the following functions and find the area under the curve on the given interval.

Step3

Graph of following function

Step4

Area=

=

Take the partial fraction of

:

=

=

Now integrate one by one

=

Apply integral substitution

=

Let u=x+3, du=dx

=

=In

=In

=

Apply integral substitution

=

Let u=x+3, du=dx

=

===

=In--In-

Step5

Area==In--In-

=

=

=)

= (by using In(27)=1.431)

==0.01676 units

Therefore, The area under the curve on the given interval is 0.01667 units.