nvect=[5,15,30,50];
fcn=@(x) 1./(1+x.^2);
xs=sym('x');
int_exact=int(fcn(xs),xs,-5,5);
err=sym(zeros(length(nvect),1));
f = matlabFunction(fcn(xs));
%a
for j=1:length(nvect)
n=nvect(j);
xj=linspace(-5,5,n+1);%-5+10/n(0:n);
xx = linspace(-5,5,1001); % points to plot approximation
intval=0;
for i=1:n+1
L_i = @(xs) 1 * ones(size(xs));
for k=i:n+1
if k~=i
L_i=@(xs) (xs-xj(k))./(xj(i)-xj(k)).*L_i(xs);
end
end
Li_int = int(L_i(xs),xs,-5,5);
intval=intval+f(xj(i)).*Li_int;
end
err(j)=abs(int_exact-intval);
end
figure(100)
semilogy(nvect,err,'k','markersize',26)
