function [J] = sect_5_prob_5_J_min_fn(lambda_0, t_0, t_f, x0,T,xair,xd,k1,c1,c2)
%   
% Written by:
% -- 
% John L. Weatherwax                2006-08-28
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% First integate the given differential equations forward in time from t=0 to t=t_f: 
% 
sol = ode23s( @(t,x) sect_5_prob_5_ode_fn(t,x, T,xair,xd,k1,c1,c2), [t_0,t_f], [x0;lambda_0] );

x_t = sol.y(1,:); % extract x(t)
lambda_t = sol.y(2,:); % extrat lambda(t)

% Second evaluate the expression for J (make sure that lambda(t_f) matches the known values): 
% 
J = 0.5 * ( lambda_t(end) - 2*c1*(x_t(end)-xd) )^2;