Using the integral of sec3 u By reduction formula 4 in

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.