solve equation with intégral with the unknown inside the integral in matlab

I'm looking for a Matlab program that will determine for which value of "tau1" this equation is verified, the problem is that one of the "R0" terminals depends on this unknown (tau1), please I need help.

[darova]

Show some of your attempts. Do you have any idea? What about fsolve?

Answer 1

[Ameer Hamza]

Try this

R1 = 7.403361345;
Bi = 100;
n = 1/2;
R0 = @(tau) sqrt(abs(tau)/Bi)*R1;

integrand = @(tau, r) (abs(tau).*R1.^2./r.^(2+n) - Bi./r.^n).^(1./n);
int_term = @(tau) integral(@(r)  integrand(tau, r), R1, R0(tau));
eq = @(tau) sign(tau)*R1*int_term(tau) + 1;
sol_tau = fsolve(eq, rand())

Result

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.

<stopping criteria details>
sol_tau =
   95.7194

[ZOUBAIR DAOUMA]

I tested this program but it does not give me the result is what you can show me how you got the result.

[Ameer Hamza]

Somewhere on your MATLAB path. You have created a script named fsolve(). fsolve() is the name of MATLAB's function. You need to rename your script. Run this line

which fsolve -all

It will show the list of all fsolve() function, which MATLAB can see. Rename the one you defined.