If you know what the curve looks like it becomes a bit easiar to evaluate the area. Look at cos^2 x - Wolfram|Alpha and let us know how you want to approach this now.
Okay there is one thing I didnt understand, sorry but i dont consider this to be a bump as I have got my answer, but I would like to ask
how you got 1/8 into 1/16 I can see that you multiplied everything within the brackets with 2. but what about 1/16?
Thanks for answers!