function [res] = optim(quadlimit)
% define the global paramters
global beta r 
global alpha n miu miuo lambda capa
% alpha = 1.2;
% beta  = 0.5;
% r     = 0.01;
% n     = 10 ;
% 
% capa = 12;
% miu   = n.^(alpha-1)/(n.^(alpha-1)+2);
% miuo   = n.^(alpha-1)/(n.^(alpha-1)+1);
% the right of the certain inequation 
rightvalue = sqrt(pi).*miu./(2.*n.^(alpha-1).*r.^(3/2));

% define the temp paramters 
a = 0;
b = quadlimit;
m = 800;
tol = 0.001;

% computer 
[R,quad,err,h]=romber('quadequ',a,b,m,tol);
quadvalue = quad;

res=sum((quadvalue-rightvalue).*(quadvalue-rightvalue));