MACHINE PROBLEM 3: Due October 7, 2020

1. Use Midpoint, Trapezoidal and Simpson's Rules with 8 sub-intervals to approximate 
the integral of sin(x) on [0,2]. 

2. Use Gaussian Quadratures with 3, 4 and 5 points to approximate the same integral.

3. Turn in a program listing and a table where the different approximations and 
their errors (compare with the exact value of the integral).

Note that you have to use 8 points for the Midpoint but 9 for the Trapezoidal and Simpson's.