function result = trap(a,b,n)

h = (b-a)/n;

x = a + h * (0: n);

fvalues = f(x);

result = h * ( fvalues(1)/2 +sum(fvalues (2 :n ))+fvalues(n+1)/2);

function y = f(x)

y=sin(sqrt(x));

R=zeros (i, i);

i=13;

disp('The result of R(1,1) in subprogram is')

k = 1; n = 2 ^(k-1);

R(k,1) = trap (a, b, n);

k =2; flag = 0 ;

while k <=13 && flag ==0

n = 2 ^ (k-1); R(k,1) = trap (a, b, n);

for j = 2:k

R(k, j )= ((4^(j-1) - 1) * R (k,j-1) + (R(k, j-1)- R(k-1, j-1)))/ (4
^(j-1) -1);

end

if ( abs ( R( k, k) -R (k-1, k-1)) <= tol)

flag = 1;

end

k=k+1;

end

if (flag == 0 )

disp ('error: if the tolerance test is not passed')

else

R( 1: j, 1 : j)

end

disp ('Enter R to find the result of matrix R (k, k)')

format long e