% Sumas de Riemann para aproximar \int_0^1 e^{\sin x} dx

clear
clc
close all
format long % para ver 16 digitos. La vista por defecto se recupera con: format short

x = linspace(0,1,1000);
plot(x, exp(sin(x)), 'LineWidth', 2);


for n = [10, 100, 1000 10000]
    
    paso = 1/n;
    subintervalos = 0:paso:1;
    suma_inf = 0;
    vec = zeros(length(subintervalos),1);

    for i = 1:size(subintervalos,2)-1
        vec(i) = exp( sin( subintervalos(i)));
        suma_inf = suma_inf +  vec(i) * paso;
    end
    
    vec(end) = vec(end-1);
    
    pause
    close all
    hold on
    plot(x, exp(sin(x)), 'LineWidth', 2);
    stairs(subintervalos, vec, 'r');
    hold off
    
    suma_inf
    
end