A)
calculate I=\int_{0}^{1}\cos(\frac{\pi}{2}x^2)
by trapeze methos in those pannels
m=1,2,4,8
?

B)
what is the best aproximation we can get from part A of the question?

solution:
the solution for part A is
http://i47.tinypic.com/2vmh4b9.jpg

my problem start with the solution of part B

http://i45.tinypic.com/b4jorq.jpg

how they find T_{2,1} for example??
how each index plays a role in the formula
by what formula they work on??

how they find out that the best approximation is  T_{3,1}
??