midpoint rule for integration

Hello, I took an entry level Matlab course last semester and for a Calculus 2 assignment I have to write a program to find the left,right,and midpoint rule as well as simpson's rule and the trapezoidal rule.

Right now I am almost done. I have the left, right, trap, and simpsons rule working. I'm trying to include the midpoint rule in this but its not working. I keep getting this error,

• Attempted to access f(1.5); index must be a positive integer or logical. *

Error in calc2 (line 68) mpr=mpr+f((2*k+1)/2)*deltax; %midpoint rule_

So far I have:

close all
clear all

disp(' ');
disp('This program will calculate the approximate integral');
disp('using the left, right, and midpoint rules, as well as');
disp('the trapezoidal and simpsons rule');
disp('-------------------------------------------------------');
disp(' ');
lower=1;
upper=2;
N=10;
% % % % % % % % lower=input('Enter the lower value of the integral: '); %lower value of integral
% % % % % % % % upper=input('Enter the upper value of the integral: '); %top value of integral
% % % % % % % % N=input('Enter the number of steps: ');
deltax=(upper-lower)/N;
x=[lower:deltax:upper]; %creates a vector of n+1 evenly spaced points
% % % % % % % % f=input('Enter the function (in proper matlab format): '); %function
f=(x.^3-1).^(1/2);
%LEFTPOINT, RIGHTPOINT MIDPOINT, AND TRAPEZOIDAL RULES
%initialize lpr,rpr,mpr,tr
lpr=0; %left point rule
rpr=0;%right point rule
mpr=0; %midpoint rule
tr=0;%trapezoidal rule
for k=1:N;  
    lpr=lpr+f(k)*deltax; %left point rule
    rpr=rpr+f(k+1)*deltax; %right point rule
    mpr=mpr+f((2*k+1)/2)*deltax; %midpoint rule  %<<<<<<<< where im running into trouble
    tr=tr+(f(k)+f(k+1))/2*deltax; %trapazoidal rule
end;

%SIMPSONS RULE
if numel(f)>1 % If the input provided is a vector
    N=numel(f)-1;
    sr= deltax/3*(f(1)+2*sum(f(3:2:end-2))+4*sum(f(2:2:end))+f(end));
else % If the input provided is an anonymous function
    sr= deltax/3*(f(x(1))+2*sum(f(x(3:2:end-2)))+4*sum(f(x(2:2:end)))+f(x(end)));
end

%fprintf for results.  
disp(' ');
fprintf('Left-endpoint approximation = %f.\n',lpr);
fprintf('Right-endpoint approximation = %f.\n',rpr);
fprintf('Midpoint approximation = %f.\n',mpr);
fprintf('Trapezoidal approximation = %f.\n',tr);
fprintf('Simpsons Rule approximation = %f.\n',sr);

Right now I have an example integral from 1 to 2 of (x.^3-1)^(1/2) but I'm going to remove those so you can enter your own values when you run the progam.

If anyone knows how I can fix that problem, I'd really appreciate it. This assignment is due friday so I have two more days. Thank you for the help!

Answer 1

[sixwwwwww]

Dear Joe, re-write f as follows:

   f = @(x) (x.^3-1).^(1/2);

Then code should work. I hope it helps. Good luck!

Answer 2

[Alperen KARAVELIOGLU]

U can also use inline method , like:

f = inline('3*.^2','x');

%hope helps..