function napaka(fun,a,b,tocna,n1,n2,d)
%napaka(fun,a,b,n1,n2,d)
%narise graf napake pri numericnem integriranju s pomocjo
%trapezne in Simpsonove metode.
%Primerja tocno vrednost integrala 
%int_a^b fun(x)dx,
%ki jo podamo s spremenljivko 'tocna'
%z rezultati funkcij 'trapez.m' in 'simpson.m' za stevilo podintervalov,
%ki gre od 'n1' do 'n2' s korakom 'd' in narise graf.

%Plots the errors of numerical integration methods of trapez.m and simpson.m
%We compare the exact value of the integral
%int_a^b fun(x)dx,
%given by the variable 'tocna' (which we must know in advance) to the results of the 
%functions trapez.m and simpson.m for numbers of subintervals  from 'n1' to 'n2'
%with step 'd'

n=n1:d:n2;%vrednosti za parameter 'n', ki nas zanimajo // values of 'n'
l=length(n);%stevilo klicov trapez.m oz. simpson.m // number of calls of the functions trapez.m and simpson.m
It=zeros(1,l);%rezerviramo prostor za rezultate // space for the results
Is=zeros(1,l);
for i=1:l
    It(i)=trapez(fun,a,b,n(i));%racunamo priblizke integralov // computing numerical approximations of integrals
    Is(i)=simpson(fun,a,b,n(i));
end
clf;
hold on
plot(n,abs(It-tocna),'b');%graf napake trapezne metode // error plot for trapez.m
plot(n,abs(Is-tocna),'r');%graf napake simpsonove metode // error plot for simpson.m