The integral is Integrate[Sqrt[1+x^3], {x, -1, 1}]. I want to create a Table with three columns and four rows that shows the midpoint, trapezoidal, and Simpson's rule approximations of the integral with n=4,8,16 and 32 subintervals. I defined the three approximations as:

f[x] := Sqrt[1 + x^3]

midptApprox[func_, {x_, a_, b_}, n_] := Module[{f, h = (b - a)/n}, f[t_] := func /. x -> t; h \!\( \*UnderoverscriptBox[\(\[Sum]\), \(i = .5\), \(n - .5\)]\(f[ a + i\ h]\)\)]

trapex[func_, {x_, a_, b_}, n_] := Module[{f, h = N[(b - a)/n]}, f[t_] := func /. x -> t; 1/2 h (f[a] + 2 \!\( \*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(n - 1\)]\(f[ a + i\ h]\)\) + f[b])]

simpson[func_, {x_, a_, b_}, n_] := Module[{f, h = (b - a)/n, wt}, wt[i_] := 3. + (-1)^(i - 1); f[t_] := func /. x -> t; If[EvenQ[n], h/3 (f[a] + \!\( \*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(n - 1\)]\(wt[i] f[ a + i\ h]\)\) + f[b]), "n must be even"]]

I was thinking to use Grid and TableForm@Table[n,f[n]},{n,4,8,16,32}] somehow but I don't know how to include the interval [-1,1].

The integral is Integrate[Sqrt[1+x^3], {x, -1, 1}]. I want to create a Table with three columns and four rows that shows the midpoint, trapezoidal, and Simpson's rule approximations of the integral with $n=4,8,16$ and $32$ subintervals. I defined the three approximations as:

f[x] := Sqrt[1 + x^3]

midptApprox[func_, {x_, a_, b_}, n_] := Module[{f, h = (b - a)/n}, 
 f[t_] := func /. x -> t; h*Sum[f[a + i*h], {i, 0.5, n - 0.5}]]

trapex[func_, {x_, a_, b_}, n_] := Module[{f, h = N[(b - a)/n]}, 
 f[t_] := func /. x -> t; (1/2)*h*
    (f[a] + 2*Sum[f[a + i*h], {i, 1, n - 1}] + f[b])]

simpson[func_, {x_, a_, b_}, n_] := Module[{f, h = (b - a)/n, wt}, 
 wt[i_] := 3. + (-1)^(i - 1); f[t_] := func /. x -> t; 
  If[EvenQ[n], (h/3)*(f[a] + Sum[wt[i]*f[a + i*h], 
           {i, 1, n - 1}] + f[b]), "n must be even"]]

I was thinking to use Grid and TableForm@Table[{n,f[n]}, {n,4,8,16,32}] somehow but I don't know how to include the interval [-1,1].