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