How to not use a for loop

Hi, Im trying to make a function that does the same task as below, but without using any loops (no for, if, ect.). I have looked on various links like the Vector Creation (https://au.mathworks.com/help/matlab/ref/colon.html) and Vectorisation (https://au.mathworks.com/help/matlab/matlab_prog/vectorization.html) but I still cant get it to work.

function I = intMidpointScalar(f, a, b, n)
% Add description, name, date, inputs, outputs
h = (b-a)/n;
I = 0;
for j = 1:n
    x = a + (j-0.5)*h;
    I = I + h*f(x);
end

With the code to call the function as:

format compact
f = @(x) sin(x).*cos(x).^2
for n = 2.^(1:6)
    I=intMidpoint(f,0,pi,n);
    nIntError=[n I I-2/3]
end

Currently I have the below function but I dont know where to go from here

function I = intMidpoint(f, a, b, n)
% Add description, name, date, inputs, outputs
h=0;
h = (b-a)/n;
I = 0;
l=1:n;
j=cumsum(l);

x = a + (j-0.5)*h;

I = I + f(x)*h;

Thanks in advance.

Answer 1

[Adam]

function I = intMidpointScalar(f, a, b, n)
    j = 0.5:n;
    h = (b-a)/n;
    
    x = a + j * h;
    I = sum( h * f(x) );
end

seems like it gives the same answer.

[Declan]

Hi I tried your function and you are missing the

h=0;
h = (b-a)/n;

At the start but the rest works thankyou!

[Adam]

Oops, yes sorry, I'll edit it now. I tested on command line and didn't put all the lines consecutively as I was testing your original version too!