Question

Find the length of the curve given by x = t

Answer 1

length of the curve,

$L=\int_{t_1}^{t_2}\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}dt$

by using above formula, we get

$L=\int_{t_1}^{t_2}\sqrt{(1)^2+(0)^2}dt\\ =\int_{t_1}^{t_2}dt\\ =t_2-t_1$