Understanding the formula $\psi = \int \kappa ds$

Consider a beam which is a perfect arc of a circle

Calculate $\int \kappa ds$ along this section. Can you relate $\phi$ to $\psi$?

Finding $v$ in terms of $\kappa$ and $x$

Consider a very small section of the beam, curved length $\delta s$ and vertical deflection $- \delta v$. Can you express $\delta v$ in terms of the other quantities?