A similar case would show that 
.
Thus, 
(b)
Note that 
. If we integrate both sides of this equation, we get 
.
Thus
But, there is one thing we have not yet considered. As 
and 
move around the circle because we end up counting each position twice. Consider the following diagram:
So our integral is actually 
These two formulas are very interesting because unlike the Equations (9) and (10), these tell us something about K itself.
Problem 15
