Question

The arc length of a curve described by r(t)=⟨cos(3t),sin(3t),3t⟩ for t∈[0,π] is

Select one:

a. 3√2π


b. 3√3π


c. √3π


d. 6√2π


e. √2π


f. 2√2π

Answer 1

$r(t)=[{\cos(3t),\sin(3t),3t}]$

$r'(t)=[{-3\sin(3t),3\cos(3t),3}]$

$\begin{vmatrix} r'(t) \end{vmatrix}=\sqrt{(-3\sin(3t)^2+(3\cos(3t))^2+3^2}=\\=3\sqrt{2}$

The length of the curve =$\int_0^\pi3\sqrt{2}dt=3\sqrt{2}\pi$

Answer: a.$3\sqrt2\pi$ .