Answer
Suppose the vector function $r(t)=\lt f(t), g(t), h(t) \gt$ on the interval $[a, b]$ , the length of the space curve is defined as follow:
$$ L=\int_a^b\sqrt {[f'(t)]^2+[g'(t)]^2+[h'(t)]^2}dt=\int_a^b\sqrt {[\frac{dx}{dt}]^2+[\frac{dy}{dt}]^2+[\frac{dz}{dt}]^2}dt$$
Work Step by Step
Suppose the vector function $r(t)=\lt f(t), g(t), h(t) \gt$ on the interval $[a, b]$ , the length of the space curve is defined as follow:
$$ L=\int_a^b\sqrt {[f'(t)]^2+[g'(t)]^2+[h'(t)]^2}dt=\int_a^b\sqrt {[\frac{dx}{dt}]^2+[\frac{dy}{dt}]^2+[\frac{dz}{dt}]^2}dt$$
