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//Simpson Rule
clc;
clear;
close();
format('v',10);
funcprot(0);
deff('[y]=f(x)','y=exp(x)');
n = [1 2 4];
a = 0;
b = 2;
h = (ones(1,3)*(b-a))./(2*n);
s(1) = h(1)*(f(a)+f(b)+4*f(h(1)))/3;
disp(s(1),'n=1');
s(2) = h(2)*(f(a)+f(b)+2*f(2*h(2))+4*(f(h(2))+f(3*h(2))))/3;
disp(s(2),'n=2');
s(3) = h(3)*(f(a)+f(b)+2*(f(2*h(3))+f(4*h(3))+f(6*h(3)))+4*(f(h(3))+f(3*h(3))+f(5*h(3))+f(7*h(3))))/3;
disp(s(3),'n=4');
exact = integrate('exp(x)','x',0,2);
disp(exact,'The exact value of intergation is :');
exact = ones(3)*exact;
err = exact-s;
disp(err,'thus corresponding errors are : ');
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