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//Newton Cotes formula
clc;
clear;
close();
format('v',9);
funcprot(0);
disp('Integral 0 to PI/4 x*cos dx');
disp('based on open Newton-Cotes formulas ');
deff('[y]=f(x)','y=x*cos(x)');
k = [0 1 2 3]
a = 0;
b = %pi/4;
h = (ones(1,4)*(b-a))./(k+2);
x0 = a+h;
xk = b-h;
k(1) = 2*h(1)*f(h(1));
disp(k(1),'k=0');
k(2) = 3*h(2)*(f(h(2))+f(2*h(2)))/2;
disp(k(2),'k=1');
k(3) = 4*h(3)*(2*f(h(3))-f(2*h(3))+2*f(3*h(3)))/3;
disp(k(3),'k=2');
k(4) = 5*h(4)*(11*f(h(4))+f(2*h(4))+f(3*h(4))+11*f(4*h(4)))/24;
disp(k(4),'k=3');
exact = integrate('x*cos(x)','x',0,%pi/4);
disp(exact,'The exact value of intergation is :');
exact = ones(1,4)*exact;
err = exact-k;
disp(err','thus corresponding errors are : ');
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