This is using arclength

### 1 Answer

arc length of a parameterized curve = ∫ (dx/dt^2 + dy/dt^2 + dz/dt^2)^1/2 dt

∫ (36 (sin^2 6t + cos^2 6t + tan^2 t) )^1/2 dt

∫ 36 sec t dt

36 ln |sec t + tan t| |0,pi/4

36 ln 3

This is using arclength

arc length of a parameterized curve = ∫ (dx/dt^2 + dy/dt^2 + dz/dt^2)^1/2 dt

∫ (36 (sin^2 6t + cos^2 6t + tan^2 t) )^1/2 dt

∫ 36 sec t dt

36 ln |sec t + tan t| |0,pi/4

36 ln 3