I have included a pdf attachment I made with mathematica to help try and explain my problem.
please help if you can..
Merlyn.
Because of the symmetries of sinusoids the integral of or over a complete period is half of the area of the rectangle of height and length equal to the period.
Look at your diagram and you will see that this is obvious (draw a rectangle around the plot of from to ).
Alternatively use the double angle formula to reduce the integral to one that can be done easily and by this tedious process you will arrive at the same result.
CB