This is the Mathematica code I have been using, basically altered so that it will compute Simpson's Rule after I have defined my function:

a = 0.6;

b = 1.5;

n = 192;

Deltax = (b - a)/n;

Sn[i_] = a + i*Deltax;

Table[xi[i], {i, 0, n}]

Sum[f[Sn[2 n - 1]], {i, 1, n - 1}]*(4 Deltax/3) +

Sum[f[xSim[2 n]], {i, 2, n - 2}]*(2 Deltax/3) + (Deltax/3)*(f[0.6] +

f[1.5])

N[%]

Unfortunately, I have no idea how to edit it in a way that will compute a table of errors.

http://archives.math.utk.edu/visual.calculus/4/approx.2/index.html

That is the webpage I am referring to for the formula of the error values. This lab is due very soon, and help would be absolutely wonderful.

The questions to my assignment are:

(a) Using Mathematica, create a table of the Midpoint, Trapezoid and \

Simpson's Rule approximations (denote them Mn, Tn and Sn \

respectively) for each of the following n: 3, 6, 12, 24, 48, 96, \

192. You should be able to alter the code above to make these.

(b) Make a corresponding table that gives the errors of these values \

(denote them EMn, ETn, ESn). To compute the error you should use \

-0.1785791162767406 as the actual value.

I have already finished (a), but I am completely stuck on (b).