Carry out the integral numerically to evaluate and A useful identity whose proof is beyond the scope of this book is

Check this formula numerically for n = 1/ 3.

Integral:

To evaluate

Step 1:

Given formula

=

Here =

Therefore

= -1

=

Step 2:

This will give

=

Calculating numerically, the result of the given integration is 2.6789

= 2.679

To evaluate

Step 1:

Given formula

=

Here =

Therefore

= -1

=

Step 2:

This will give

=

Calculating numerically, the result of the above integration is 1.3541

= 1.354

To Verify The Results

Step 1:

Given formula

=

For n = the above equation becomes

=

= 3.628