Exercise 1.  Calculate the following.  

1 (a).  .  

Solution 1 (a).

See text and/or instructor's solution manual.

Use the general formula  .  

For  ,  use the formula  .  

Here we have  ,  and  ,  so that

        .

For  ,  use the formula  .  

Here we have  ,  and  ,  so that

        .

Therefore,

           

We are done.   

Or, we could just expand the quantities

,   and

.

Then,

          

We are done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell