Multiple ways to solve this. First the easy, just as a numerical integration using a trapeziodal rule.
INT cannot solve the problem in symbolic form. Oh well. I had a funny feeling int might have issues.
Rsym = exp(-(T./eta).^beta);
int(Rsym)
ans =
So we see that int gave up. But that does not mean we need to give up too. We can still solve the problem easily enough. Use ode45. Effectively, if we wish to integrate R from 0 to t, this is equivalent to solving the simple first order ODE, of the form
dy/dt = R(t) = exp(-(t./eta).^beta)
You should recognize this as a basic way to perform a cumulative integration. So set this up as an ODE, then apply ODE45 to the problem.
odefun = @(t,y) exp(-(t./eta).^beta);
[Tout,Yout] = ode45(odefun,tspan,y0);
Again, quite easy to solve. Remember this trick when you need to perform a cumulative integration. Just because you see an integral sign in there, it does not mean you need to use integral or int.
