Length Of A Helix

Calculus Level 4

Consider the cylindrical helix in \(\mathbb{R}^3\) whose equations are

\[x = 3\cos(t) \hspace{.4cm} y = 3\sin(t) \hspace{.4cm} z = 4t\]

What is the length of this helix from \(t = 0\) to \(t = 403\)?