PlanetMath article, the method is quite simple, if you have problems with that tell us what they are and we will help you with those specific problems.
Ok, this is what I did and I'm pretty sure I did it right, but I am getting a different answer from what is in the solution's manual.
pi/48 * (f(0) + 4*f(pi/16) + 2*f(2*pi/16) + 4*f(3*pi/16) + 2*f(4*pi/16) + 4*f(5*pi/16) + 2*f(6*pi/16) + 4*f(7*pi/16) +f(8*pi/16) )
If I do all this, I get 0.026272 which is exactly what the answer would be if you integrated the problem, but the answer is supposed to be 1.37076. What am I doing wrong?
Right. When I just calculated it with my values, I got an answer of 1.305314.
One thing that can be throwing off the answer is calculating the first term - f(0). Sin 0/0 is not possible, so is that where the "x=0 to be 1" condition comes in? (i.e plugging in 1 to the to the function instead of 0?) If that is the case, I get a closer number in 1.36038, but still not quite there.