// script para regras de integracao

clear;

a = 0;
b = 10;
i_max= 50;

p=[0 0 0];
q=[0 0 0 ];

function y = ff(xx)
y = exp(xx);
endfunction
fe = %e^(b) - %e^(a);


// regra do trapezio
for i=1:i_max
//i = 1;
N = 2*i;
h = (b-a)/(2*N);
m(1:(2*N-1))=2;
m=[1; m; 1];
x = [a:h:b];
f = ff(x);
ar = f*m*h/2;
dif = abs(ar - fe);
p=[p; h ar dif];
end

// regra de Simpson
clear m x f ar dif;
for i=1:i_max
//i = 1;
N = 2*i;
h = (b-a)/(2*N);
m(1:2:(2*N-1))=4;
m(2:2:(2*N-2))=2;
m=[1; m; 1];
x = [a:h:b];
f = ff(x);
ar = f*m*h/3;
dif = abs(ar - fe);
q=[q; h ar dif];
end

pq=[p(:,3) q(:,3)];

clf();
plot2d(p(2:10,1),pq(2:10,:),rect=[0,0,max(p(:,1)),max(p(:,3))],style=[2,3])  
//plot2d(p(2:10,1),pq(2:10,:),rect=[0,log(min(q(2:10,3))),max(p(:,1)),log(max(p(:,3)))],style=[2,3],logflag="nl")