clear all clc
prompt = 'Enter n: ';
n = input(prompt);
simprl(@(x)(exp(-x^2)),0,1,n);
function s=simprl(f,a,b,n)
array1 = ones(1,n);
array2 = ones(1, 2*n);
array3 = ones(1,n);
array4 = ones(1,n);
fun = @(x)(exp(-x.^2)); true = integral(fun,a,b);
n = n * 2;
even =0;
odd = 0;
y0 = f (a);
yn = f (b);
x = 0;
h=(b-a)/( n / 2);
for i = 0: (( n) + 1) x=0;
        even = 0;
        odd = 0;
        h=(b-a)/(i + 1);
        for j = 1:i
x = x + a + h; r = mod(j,2);
         if (r == 0)
            even = even + f(x);
else
end end
end
I = (h / 3) * ((y0 + yn) + 2 * even + 4 * odd);
odd = odd + f(x);
fprintf('Value after %i', n/2 ) fprintf(' iterations: %.16f \n', I);
fprintf('True value for the integral: %.16f' , true);
even =0;
odd = 0;
y0 = f (a);
yn = f (b);
x = 0;
h=(b-a)/( n );
for i = 0: ((2 * n) + 1) x=0;
        even = 0;
        odd = 0;
        h=(b-a)/(i + 1);
        for j = 1:i
x = x + a + h; r = mod(j,2);
         if (r == 0)
            even = even + f(x);
else
end end
y = (h / 3) * ((y0 + yn) + 2 * even + 4 * odd); array2(1, i + 1) = y;
end
even =0;
odd = 0;
y0 = f (a);
yn = f (b);
x = 0;
h=(b-a)/(n / 2);
for i = 0: n - 1
        x=0;
        even = 0;
        odd = 0;
        h=(b-a)/(i + 1);
odd = odd + f(x);

for j = 1:i
x = x + a + h;
         r = mod(j,2);
       if (r == 0)
          even = even + f(x);
else
end end
y = (h / 3) * ((y0 + yn) + 2 * even + 4 * odd); array1(1, i + 1) = y;
array4(1, i + 1) = i;
l = array1(i + 1);
m = array2(2 * (i + 1));
rich= ( ((2^8)*m)-l)/((2^8)-1); error = (rich - true ) / true;
error = abs(error);
array3(1, i + 1) = error;
end
    a = array3(2:2:end);
    b = array4(2:1:(n/2)
    loglog(b,a)
        title('Composite
xlabel('iterations') ylabel('error %');
end
+ 1);
Simpsons 1/3 rule error %'); ;