Why I keep getting error on this Numerical Integration problem ?

syms x

f=((cos(log(x)./x))./x);

for i=1:1000

a=a+0.001*i;

b=b+0.001*(i+1);

s1=int(@f,x,a,b);

i=i+s1;

end

New to MATLAB. Can anyone please help me why can't I execute the code ?

Error: "f" was previously used as a variable, conflicting with its use here as the name of a function or command.

Answer 1

[Star Strider]

Do not use the function handle representation here.

Just use:

s1=int(f,x,a,b);

It would be preferable to define ‘f’ as a symbolic function:

f(x)=((cos(log(x)./x))./x);

Also, define ‘a’ and ‘b’ with some initial values before the loop. Not doing that will throw an error, since they are calculated recursively.

Answer 2

[John D'Errico]

Your problem is you are mixing up numerical integratino and symbolic integration. What are you trying to do?

A numerical solution might look like:

f = @(x) ((cos(log(x)./x))./x);
x = linspace(0,1,1001);
trapz(x,f(x))
ans =
   NaN

It fails to generate anything useful, as I would expect based on what I write below.

A symbolic solution might look like:

syms x
K = ((cos(log(x)./x))./x);
int(K,0,1)
ans =
int(cos(log(x)/x)/x, x, 0, 1)

int returns no solution, which suggest only that it was unable to do the symbolic integral. We might try vpaintegral...

vpaintegral(K,0,1)
Error using sym/vpaintegral (line 202)
Failed precision goal. Try using 'MaxFunctionCalls'. 

But it also fails. Why? To understand that, we need to look at your kernel.

f = @(x) ((cos(log(x)/x))/x);
fplot(f,[0,1])

UGH. A highly oscillatory integrand, that oscillates between -inf and inf near zero. You don't seriously want to integrate this, do you? It does look like Wolfram Alpha gves an answer, though I would want to verify that before I trust it very far.

integral_0^1 cos(log(x)/x)/x dx≈0.3233674...

Hmm. Suppose we try a transformation?

u = log(x)

then we have

du = dx/x

the integral becomes

int(cos(u*exp(-u)),-inf,0)

It looks a little simpler, but it is still highly oscillatory on that now infinite interval.

Again however, int and vapintegral will fail to yield a result that I can trust, and Wolfram Alpha gives a completely different answer. That suggests the answer is not as easy to find as you might think.