Find the length of the curve. r(t) = cos(6t) i + sin(6t) j + 6 ln cos t k, 0 ≤ t ≤ π/4?

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

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