R = 1;
z = eps:0.001:R;
A2 = 0.001;
g = 9.8;
A1 = 2*pi*R*z-pi*z.*z;
t = - (A1./(A2*sqrt(2*g)*sqrt(z))).*sqrt(1-A2*A2./(A1.*A1));
s = simpsons(t,R,0,1000)
plot(z,t)