Calculus 8th Edition

a) Let the length of the curve $C$ be $L$ which inscribes polygons $A_i$. Such as: $L=\lim\limits_{n \to \infty} \Sigma_{i=1}^n|A_{i-1}A_i|$ b) Formula to calculate the length of a smooth curve is given as: $L=\int_a^b\sqrt {1+[f'(x)]^2} dx$ c) Formula to calculate the length of a smooth curve when $x$ can be given as function of $y$ as: $L=\int_c^d\sqrt {1+[g'(y)]^2} dx$; Here $x=g(y)$