O14-908

> restart:
> f:=t->exp(-t^2):a:=0:b:=2:
> der:=diff(f(t),t$4);

                         2        2       2        4       2
         der := 12 exp(-t ) - 48 t  exp(-t ) + 16 t  exp(-t )

> M:=maximize(der,t=0..2);

                               M := 12

> E:=evalf(2^5*M/2880);valapp:=evalf((b-a)*(f(a)+f(b)+4*f((a+b)/2))/6);valexact:=evalf(int(f,a..b));

                           E := .1333333333


                        valapp := .8299444678


                       valexact := .8820813910