Thread: length of a curve

find the length of the curve r(t)=2t^(3/2)i + cos(2t)j + sin(2t)k 0<t<1.

then the length of the curve is

In general

s= integral (sqrt[(dx/dt)^2 +(dy/dt)^2 + (dz/dt)^2]dt)

here s = int (sqrt[9t+ 4])

Let u = 9t + 4

du = 9dt

s = 1/9intsqrt(u) = 2/27(9t+4)^(3/2) from 0 to 1

s = 2/27(13^3/2- 8)