PX275 - B2b - simple examples of line integrals

length of a line

s = \int_{s_{1}}^{s_{2}} d s

\begin{aligned} d s & = d x \sqrt{1 + {(\frac{d y}{d x})}^{2}} \\ = d x \sqrt{1 + m^{2}} \\ ⟹ s & = \int_{x_{1}}^{x_{2}} \sqrt{1 + m^{2}} d x \end{aligned}

d s^{2} = δ ρ^{2} + (ρ δ ϕ)^{2}

s = \int_{ϕ_{1}}^{ϕ_{2}} ρ d ϕ