Help needed with errors in trapezoidal formula for integration

I have gotten my code working to an extent however the code takes forever to work and I was hoping someone could help me check if this is the best way to do it as the error needs to be less than 0.001%. Thanks for any contributions anyone can give.

function  trapezoidal(N)
clc
%%Limits & sub-intervals
a = 0;
b = 0.449933;

   if nargin == 1
      n = N;
  else
      n = 100;
  end
  fprintf('\n Limits[%g,%g] \n',a,b);

   % h = (b-a)/n;
  %%Integral Aproximation (Composite Trapezoidal Rule)
  integral = 0;
  for j=1:n
      ri=2^j;
      h = (b-a)/ri;
      for i = 1:ri
          r_left = a+(i-1)*h;
          r_right = a+i*h;
          % Functions
          f_left = f(r_left);
          f_right = f(r_right);
          % Integral
          integral = integral+(h/2)*(f_left+f_right);

      end
      % Print the approximation to the value fo the intragral

      %%Calculating Relative Error
      if j > 1

          errorrel = ((integral-integralo)*100/integral);
          %%Loop Termination
          if abs(errorrel) < 0.001
              break       
          end
      fprintf('\nMidpoint approximation to integral using %g subintervals is  %g with Error %g\n',ri,integral,errorrel);
      end
      integralo = integral;
  end
  end

   function [f_value] = f(r)
  %%Variables
  k = 2;
  n = 0.85;
  pgrad = -80;
  R = 0.449933;
  %%Equation
  f_value = 2*pi*((-pgrad/(2*k))^(1/n))*((R^(1+1/n)-r^(1+1/n))/(1+1/n))*r;

   end