I know that we can calculate Jacobi amplitude function using the following equations:
$$\operatorname{am}(u,k) = \phi = F^{-1}(u,k)$$
$$ u=F(\phi,k) = \int_0^{\phi} \frac{d\theta}{\sqrt{1-k^2\sin^2\theta}} $$
But I do not really understand how to calculate it precisely.
Let's assume that $u=3$ and $k=0.2$.
I assume that I have to calculate the following expression, but I do not really understand how to calculate it.
$$3 = \int_0^{\phi} \frac{d\theta}{\sqrt{1-0.2^2\sin^2\theta}} $$
I would like to calculate it using c++ without using libraries.
I would really appreciate it, if you could how I could calculate it. I do not need the c++ code, I just need a proper explanation