MATH-3190 Lecture 29: 29 equivalence classes

to (0, 0). 4. Evaluate Jc F dr where C has parametrization r() (cos t. sint, 2t) for O SisT and F(a

4. Find Jc F.F for each possible combination of F, C below: a) C is the path from (0.0.0) to (1, 1, 1) along r(t) = 〈t, t, t*), 0-t-1 b) C = Cl +C2, where G is the line segment from (0,0,0) to (0,0,1) and C2 is the line segment from (0, 0,1) to (1, 1,1). i)「(x, y, z)= 〈y, x,z) ii) F(x, y, z) = 〈y + z, z + x, x + y〉

Consider F and C below. F(x, y) = xy,2 i + x2yj C: r(t) = , 0 (a) Find a function f such that F = t 1 (b) Use part (a) to evaluate Jc Vf dr along the given curve C.