%% Monte Carlo integration
% This code lets you approximate the area under the graph of x^2 for x
% between 0 and 1, so the integral of x^2 from 0 to 1 by choosing n random
% points in the unit square and calculating the fraction of points which 
% are under the graph. The notation x.^2 means square each component of the
% vector x. 
n = 10000; % set the value of n
x = rand(1,n); % choose n random x values
y = rand(1,n); % choose n random y values
sum(y<x.^2)/n % test each component (x(i),y(i)) to see whether it is under 
              % the graph, and if so add 1 to the sum.