A curious student wrote on 04/15/2011 11:18 AM:
> Hi Professor!
> About part b) of problem 3, where we are to show that the integral
> equals 1 when i=j and 0 when i does not equal j, should I go about
> solving each integral for i=1, 2, 3, 4; or is there a simpler approach
> where I can be general that will suffice? Thanks and have a great weekend!

That is a good question.

Please do not do the four cases separately.  Possible, but not optimal.

You can work out the integral with x_i, y_i and z_i left as symbols. The integral result will, then, be a (simple) function of these symbols.  Once you have that result, it should be apparent that it reduces to a simple number for all cases of i, i.e. for all possible sets of values for x_i, y_i, z_i.

Let me know if more questions arise,
Sam