(a)

> with(plottools):

> f:=x->exp(x-1);
n:=4;
a:=1;
b:=5;
h:=(b-a)/n;

> fplot:=plot(f(x),x=a..b,color=black,title="Regra do trapézio composta"):
l1:= polygon([[a,0],[a+h,0],[a+h,f(a+h)],[a,f(a)]],color=gray,linestyle=2,thickness=1):
l2:= polygon([[a+h,0],[a+2*h,0],[a+2*h,f(a+2*h)],[a+h,f(a+h)]],color=gray,linestyle=2,thickness=1):
l3:= polygon([[a+2*h,0],[a+3*h,0],[a+3*h,f(a+3*h)],[a+2*h,f(a+2*h)]],color=gray,linestyle=2,thickness=1):
l4:= polygon([[a+3*h,0],[a+4*h,0],[a+4*h,f(a+4*h)],[a+3*h,f(a+3*h)]],color=gray,linestyle=2,thickness=1):
display(fplot,l1,l2,l3,l4);

> TrComposta(f,a,b,4);
SiComposta(f,a,b,4);
sol:=evalf(int(f(x),x=a..b));

> n:=8;
h:=(b-a)/n;
Ih:=TrComposta(f,a,b,n);

Regra de Runge (Regra do trapézio composta)

Regra de Runge (Regra de Simpson composta)