% MONTE2D Example of Monte Carlo integration in 2D
% Let R be the region in the first quadrant which is
% between y = x^2 / 4 (i.e. above it) and y = e^-x
% (below that). Compute
% /
% | cos(x^3 + y) dx dy
% / R
% Note that we see that R is inside the rectangle
% [0,2] x [0,1] which has area A = 2.
N = 1000000;
A = 2;
S = 0; % the sum
for j = 1:N
x = 2 * rand; y = rand;
if (y > x^2/4) & (y < exp(-x))
S = S + cos(x^3 + y);
end
end
result = S * A / N