% GLINT  Gauss-Legendre integral of sin(t)

%3pt Gauss-Legendre rule from top of page p. 341
x=[-sqrt(3/5) 0 sqrt(3/5)]; c=[5 8 5]/9;

h=0.1;  a=0:h:6.4;
sum=0; S=[sum];
for j=1:length(a)-1
    %next two lines do formula (5.19)
    f=sin((h/2)*x+(a(j)+a(j+1))/2);
    sum=sum+(h/2)*c*f';
    S=[S sum];
end

% report answer
S
err=max(abs(S-(1-cos(a))))