Simpson's Rule is named after an English mathematician from the 18th century. In this module, you looked at how Simpson's Rule can be applied. In your initial post to the discussion, respond to the following: Evaluate the integral from zero to pi of the function f(x) = sin(x) using both the trapezoidal rule and Simpson's rule for two different values of n. Which method produces a more accurate estimate for the integral? Why? Finally, be sure to respond to at least two of your peers' discussion posts.

So far I have:

Using the trapezoidal rule, the integral from zero to pi of the function f(x) = sin(x) can be approximated as:

n = 4: (pi/4)[sin(0) + 2sin(pi/4) + 2sin(pi/2) + sin(3pi/4)] 1.896118

n = 8: (pi/8)[sin(0) + 2sin(pi/8) + 2sin(pi/4) + 2sin(3pi/8) + 2sin(pi/2) + 2sin(5pi/8) + 2sin(3pi/4) + 2sin(7pi/8)] 1.982887

Using Simpson's rule, the integral can be approximated as:

n = 4: (pi/12)[sin(0) + 4sin(pi/4) + sin(pi/2)] 2.002898

n = 8: (pi/24)[sin(0) + 4sin(pi/8) + 2sin(pi/4) + 4sin(3pi/8) + sin(pi/2)]

but that's as far as I've gotten I'm not sure what n=8 for the Simpson rule would be. I just need help finding the solution for the n-8 under the simpson rule.