Can someone please tell me where I'm wrong so that I can correct it

 M = 2.5
fun1 = @(y) 1./y.*((sqrt(M^2 - 1)- cot(x))); 
Km = integral(fun1,0,2.5);

above is my code an I need to know how to use the integral function on it. I keep getting this set of errors

Error in Intergral_test>@(y)1./y.*((sqrt(M^2-1)-cot(x)))

Error in integralCalc/iterateScalarValued (line 314)
                fx = FUN(t);

Error in integralCalc/vadapt (line 132)
            [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)
        [q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 88)
Q = integralCalc(fun,a,b,opstruct);

Error in Intergral_test (line 3)
Km = integral(fun1,0,2.5); %returns C-.

Answer 1

[John D'Errico]

You don't think having

- cot(x)));

in an integral with a kernel that is a function of y will cause a problem? :)

If x is symbolic, know that integral CANNOT solve a symbolic problem. If x is something else, I would point out that you have not defined it, in what you have shown us.

[Manil Athapattu]

well technically I'm try to code these two equations. where r is your y and theta is your x and d(theta +/- v) is a constant. Even if i do define all variables I keep getting errors.

m = 2.5
x = 0.01305
const = @(y) 1./(sqrt(m.^2 - 1)- cot(x)).* 1/y;
Kp = integral(const,0,2.5);

it tells me that the matrix dimensions must agree.

[John D'Errico]

Ok, but then you need to appreciate the difference between / and ./, after all, you knew to use .^ as well as ./ in the beginning, so why not ./ at the very end of that expression?

Of course, then you will get another error, since your kernel has a singularity at zero, where it is infinite. So, even if you do fix that problem, you will next get another error.

To be honest, this all seems a bit silly, since you are effectively trying to use numerical integration to integrate K/y, where K is a constant, and to do so over the domain [0,2.5]. The integral is inf, or, if you prefer, K*inf, which is still inf.

So I think you need to go back and understand more deeply what that .png is trying to tell you to do.

[Manil Athapattu]

thanks a lot mate figured it out, my bad did not think that it would go to infinity at 0, either way i used 0.000001 which is pretty small. plus that constant i get is going to be used in some other equations so that is makes sense.

[John D'Errico]

But 0.0000001, or whatever will create a arbitrarily large result and very different, based on whether you decided to use 0.0001, 0.0000000001, whatever. So just using a small number is not the right way to solve this, since exactly what number you choose as "small" will give you absurdly different results.

The .png suggests this is something that lives along some path. What path, we don't know, since we have been given only one single expression from a book or paper.