%% use symbolic expression
syms x

%% output data in long format , namely, show more digits
format long

%% specify the function 
y = cos(x);

%% plot function y on [0, 2*pi]
ezplot(y, [0, 2*pi]); 


%% get the 3rd Taylor polynomial
P3 = taylor(y,4)

%% evaluate P3 at x = 0.01
subs(P3,x,0.01);

%% integrate P3

int_P3 = int(P3)

%% evaluate definite the integral of P3 on [0, 0.01]
i1 = eval(int(P3, x, 0, 0.1))
i2 = eval(int(y, x, 0, 0.1))

%% determine the error
err = abs(i1-i2)
%subs(int_P3, 0.01) - subs(int_P3, 0.0)
%cos(0.01)