Can someone check my for loop?

I am suppose to create a function m file called mylength(f,a,b,n) which takes four inputs:

f: A function handle.

a: A real number.

b: A real number.

n: A positive integer.

Note: You may assume that f(x) is differentiable on [a, b] and that a < b.

Does: Calculates the length of f(x) on [a, b] using the formula L = the integral from a to b

of the square root of (1 + f′(x)^2 dx) but with the integral approximated using a for loop to

calculate a left sum with [a, b] divided into n subintervals.

Returns: This approximated length.

This is my code:

function l=mylength(f,a,b,n);
syms x;
for w=(a:(b-a)/n:b);
    y=subs(f(x),w);
    l=vpa(int(sqrt(1+(diff(f(x)))^2),a,w));
    a=w;
end
end

Here is sample data provided by my professor along with the correct answer to the sample data.

a = mylength(@(x) x^2,0,2,5)

a = 4.0480127986983730101003658887008

a = mylength(@(x) sin(x),pi,2*pi,10)

a = 3.820197787492867218055528594355

My code is not getting these answers. I am getting a =1.4947291280552747936216400307868, and a =

0.44067936609310253784512035349948 respectively. Can someone tell me why my code is not producing the correct answers? Where is my code wrong? I think it has something to do with calculating the left sum, I don't think my code is written correctly to calculate the left sum.

Answer 1

[Star Strider]

You need to sum ‘l’ (lower case ‘L’). Then it works.

Doing that, I got your professor’s answer for ‘sin(x)’ but not for ‘x^2’. I suspect that with your same code giving the correct answer for one and the incorrect answer for the other, one of your professor’s answers is incorrect.

[Bri]

I'm sorry, I don't understand what you mean by sum 'l'. Can you please explain?

[Star Strider]

Yes.

Summing ‘l’ in your loop involves two changes:

syms x;
w=a:(b-a)/(n-1):b;
l = 0;
for k1 = 1:length(w)
    y=subs(f(x),w(k1));
    l = l + vpa(int(sqrt(1+diff(f(x))^2),a,w(k1)));
    a=w(k1);
end

Initially set ‘l’ to zero and then add to it in each iteration of the loop. It has the correct answer at the end of the loop.

[Bri]

Thanks

[Star Strider]

My pleasure!