The total curvature of the portion of a smooth curve that

Last updated: 6/16/2023

The total curvature of the portion of a smooth curve that runs from s So to S So can be found by integrating x from S 4 1 ds Sxds Sxrdt x v dt 0 to So to s If the curve has some other parameter say t then the total curvature is K where to and t correspond to so and s a Find the total curvature of the portion of the helix r t 8 cos t i 8 sin t j tk 0sts 4 b Find the total curvature of the parabola y 3x x a Find the total curvature of the portion of the helix r t 8 cos t i 8 sin t j tk 0 t 4x The total curvature is Type an exact answer using as needed