Integration by Simpsons 1/3 rule

%% Write a MATLAB program to integrate the equation f(x) = dx/(1+x^2) within

%% the limits of 0 to 6 by taking 6 subintervals by using simpsons 1/3 rule.



% Given

x0 = 0;

xn = 6;

n = 6;

h = (xn-x0)/n;

y0 = 1/(1+x0^2);

yn = 1/(1+xn^2);

% sum of integral terms is given by y0+yn+4*(y1+y3+....yn-1)+2*(y2+y4+...Yn-2)

s = 0;

for i = 1:2:n-1

s = s + 4*1/(1+(x0+i*h)^2);

end

for i = 2:2:n-1

s = s + 2*1/(1+(x0+i*h)^2);

end

s = s+y0+yn;

% integral is given by h/3(sum of integral terms)

integral = (h/3)*s;

fprintf (' The integral by simpsons 1/3 rule is = %2.5f \n',integral);