Something

Iexa:=int(2+3*x,x=1..2);
                             Iexa := 13/2

> errortrap:=n->value(abs(Iexa-trapezoid(2+3*x,x=1..2,n)));

  errortrap :=

        n -> value(| Iexa - trapezoid(2 + 3 x, x = 1 .. 2, n) |)

> errortrap(4);

                                  0

> Iexb:=int(x^2,x=1..2);

                             Iexb := 7/3

> errortrap:=n->value(abs(Iexb-trapezoid(x^2,x=1..2,n)));

                                               2
   errortrap := n -> value(| Iexb - trapezoid(x , x = 1 .. 2, n) |)

> errortrap(4);

                                 1/96

> Iexc:=int(3+x+x^2,x=1..2);

                             Iexc := 41/6

> errorsimp:=n->value(abs(Iexc-simpson(3+x+x^2,x=1..2,n)));

  errorsimp :=

                                             2
        n -> value(| Iexc - simpson(3 + x + x , x = 1 .. 2, n) |)

> errorsimp(4);

                                  0

> Iexd:=int(x^3,x=1..2);

                             Iexd := 15/4

> errorsimp:=n->value(abs(Iexd-simpson(x^3,x=1..2,n)));

                                              3
    errorsimp := n -> value(| Iexd - simpson(x , x = 1 .. 2, n) |)

> errorsimp(4);

                                  0

> Iexe:=int(x^4,x=1..2);

                             Iexe := 31/5

> errorsimp:=n->value(abs(Iexe-simpson(x^4,x=1..2,n)));

                                              4
    errorsimp := n -> value(| Iexe - simpson(x , x = 1 .. 2, n) |)

> errorsimp(4);

                                1/1920

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