Answer
a) See the explanation below.
b) See the explanation below.
c) See the explanation below.
Work Step by Step
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 $x=g(y)$
