//Exercice IV
clf;
n = 750;
a = -2;
b = 2;
X = [];
Y = [];
Z = [];

for i = 1:n,
u = ((b-a)*rand())-2;
X = [X, (b-a)*cos(%pi*u)*sqrt(4-u^2)];
Y = [Y, (b-a)*u^2*sqrt(4-u^2)];
Z = [Z, (b-a)*u^4*sqrt(4-u^2)];
end

IX = integrate('cos(%pi*u)*sqrt(4-u^2)','u',a,b);
IY = integrate('u^2*sqrt(4-u^2)','u',a,b);
IZ = integrate('u^4*sqrt(4-u^2)','u',a,b);

SFX = cumsum(X)./(1:n);
SFY = cumsum(Y)./(1:n);
SFZ = cumsum(Z)./(1:n);

plot2d(1:n,SFX,1);
plot2d(1:n,SFY,5);
plot2d(1:n,SFZ,9);

plot2d([1,n],[IX,IX],3);
plot2d([1,n],[IY,IY],6);
plot2d([1,n],[IZ,IZ],2);


xselect()