//Gaussian Quadrature Rule
clc;
clear;
close();
format('v',10);
funcprot(0);
disp('Integral 0 to 2 exp(x)dx');
deff('[y]=f(t)','y=exp(t+1)');
b = 1;
a = -1;
x = poly(0,'x');
p = x^4 - 6*x^2/7+3/35;
x1 = roots(p);
A = [1 1 1 1;x1';(x1.^2)';(x1.^3)'];
B = [(b-a);(b^2-a^2)/2;(b^3-a^3)/3;(b^4-a^4)/4];
C = inv(A)*B;
I = C(1)*f(x1(1))+C(2)*f(x1(2))+C(3)*f(x1(3))+C(4)*f(x1(4));
disp(I,'Calculated integration : ');
exact = integrate('exp(x)','x',0,2);
disp(exact,'The exact value of intergation is :');
err = exact - I ;
disp(err,'Error : ' );