function simpsonsIntegration
x=[2.5, 2.0, 3.0, 1.5, 3.5, 1.0, 4.0, 0.5, 4.5, 0.0, 5.0];
y=[2.14, 1.73, 2.59, 1.60, 2.66, 1.82, 1.80, 2.27, 0.26, 2.67, 0.45];
x0 = 2.5;
n = size(x, 1);
if n == 1
n = size(x,2);
end
for i = 1:n
D(i,1) = y(i);
end
for i = 2:n
for j = 2:i
D(i,j)=(D(i,j-1)-D(i-1,j-1))/(x(i)-x(i-j+1));
end
end
fx0 = D(n,n);
for i = n-1:-1:1
fx0 = fx0*(x0-x(i)) + D(i,i);
end
formula =@(z) D(1,1)+(D(2,2)*(z-x(1)))+(D(3,3)*(z-x(1))*(z-x(2)))+(D(4,4)*(z-
x(1))*(z-x(2))*(z-x(3)))+(D(5,5)*(z-x(1))*(z-x(2))*(z-x(3))*(z-x(4)))+(D(6,6)*(z-
x(1))*(z-x(2))*(z-x(3))*(z-x(4))*(z-x(5)))+(D(7,7)*(z-x(1))*(z-x(2))*(z-x(3))*(z-
x(4))*(z-x(5))*(z-x(6)))+(D(8,8)*(z-x(1))*(z-x(2))*(z-x(3))*(z-x(4))*(z-x(5))*(z-
x(6))*(z-x(7)))+(D(9,9)*(z-x(1))*(z-x(2))*(z-x(3))*(z-x(4))*(z-x(5))*(z-x(6))*(z-
x(7))*(z-x(8)))+(D(10,10)* (z-x(1))*(z-x(2))*(z-x(3))*(z-x(4))*(z-x(5))*(z-
x(6))*(z-x(7))*(z-x(8))*(z-x(9)))+(D(11,11)*(z-x(1))*(z-x(2))*(z-x(3))*(z-x(4))*(z-
x(5))*(z-x(6))*(z-x(7))*(z-x(8))*(z-x(9))*(z-x(10)));
derivativeFormula =@(z) (D(2,2)+(D(3,3)*(z-x(2)))+(D(4,4)*(z-x(2))*(z-x(3)))+
(D(5,5)*(z-x(2))*(z-x(3))*(z-x(4)))+(D(6,6)*(z-x(2))*(z-x(3))*(z-x(4))*(z-x(5)))+
(D(7,7)*(z-x(2))*(z-x(3))*(z-x(4))*(z-x(5))*(z-x(6)))+(D(8,8)*(z-x(2))*(z-x(3))*(z-
x(4))*(z-x(5))*(z-x(6))*(z-x(7)))+(D(9,9)*(z-x(2))*(z-x(3))*(z-x(4))*(z-x(5))*(z-
x(6))*(z-x(7))*(z-x(8)))+(D(10,10)*(z-x(2))*(z-x(3))*(z-x(4))*(z-x(5))*(z-x(6))*(z-
x(7))*(z-x(8))*(z-x(9)))+(D(11,11)*(z-x(2))*(z-x(3))*(z-x(4))*(z-x(5))*(z-x(6))*(z-
x(7))*(z-x(8))*(z-x(9))*(z-x(10))));
deriv=derivativeFormula(x0);
D
fprintf('The value of the derivative of x = %f is %f', x0 , deriv);
fplot(formula, [-0.1, 5.1])
end
