if c is a smooth curve given by a vector function rstd, a < t < b, and v is a constant vector, show that i x − y s y 2 1 z 2 dsx, y, zd ds c c c find the moments of inertia for the wire in exercise 35. 39. find the work done by the force field fsx, yd − x i 1 s y 1 2d j in moving an object along an arch of the cycloid rstd − st 2 sin td i 1 s1 2 cos td j 0 < t < 2 40. f ind the work done by the force field fsx, yd − x 2 i 1 ye x j on a particle that moves along the parabola x − y 2 1 1 from s1, 0d to s2, 1d. 41. find the work done by the force field fsx, y, zd − kx 2 y 2 , y 2 z 2 , z 2 x 2 l on a particle that moves along the line segment from s0, 0, 1d to s2, 1, 0d. y c v ? d r − v ? frsbd 2 rsadg
