Find the length of the curve rt

Solution

length = integral of (dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2
dx/dt = 12, dy/dt = 12t, dz/dt = 6t
length = integral of (144 + 144t + 36t^2)
length = 6 integral of t^2 + 4t+4)
length = 6 integral of (t+2)dt
integrating
length = 6(t^2/2 + 2t) + C
length = 3t^2 + 12t + C