Find the arc length of F from 000 to 3pi3pi20 Where t2ttsint

Solution

x = 2t,y = tsint, z = tcost
dx/dt = 2, dy/dt= sint + tcost, dz/dt = cost - tsint
arc length = integral of (dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2
arc length = integral of (4 + sin^2t + 2tsintcost + t^2cos^2t + cos^2t - 2tsintcost + t^2sin^2t)
arc length = integral of (4 + 1 + t^2)
arc length = integral of (t^2+5)
integrating wrt t
arc length = t/2 (t^2+5) + 5/2 ln|t + (t^2+5)| + C
you can apply the limits now