% matlab code
% use Simpson's method for integration
f=inline("cos(10*x)");
x0=-1;
x1=1;
N=1000;
dx=(x1-x0)/N;
S=0.0;
for i=1:N/2
xx1=x0+dx*(2*i-2);
xx2=x0+dx*(2*i-1);
xx3=x0+dx*(2*i);
S=S+1/3*(f(xx1)+4*f(xx2)+f(xx3))*dx;
end
err=sin(10)/5-S;