Question

Find the line integrals of F=3yi + 4xj + 2zk from (0,0,0) to (1,1,1) over each of the following paths. a. The straight-line path Cy: r(t) = ti + tj + tk, Osts 1 b. The curved path Cz: r(t) = Osts1 c. The path C, UC, consisting of the line segment from (0,0,0) to (1,1,0) followed by the segment from (1,1,0) to (1,1,1) (0,0,0) (1.1.1)

Answer 1

të 39,9x2 YU): <titit. Ostel D Flow) = <34,46, 26). Fakt) = 411 Flyik). Y'!) = (36,4t, 2t>.<1,1,17 = 2t+44 +44 = 97 ffdre ' Forcm).xle) dt = f'atdt: (98) = 1 rit) = <t, t'; t">, ostel, Flret).d'et) = < t, 45, 8e"><1,20,48> = 3t+84 +84? = 1lt+847 {Fidrs s'fore). Yleedt - J'(ne + st") dt olct) =(yat, 4t = 441-0)+ (60) – ' G: 09010) to (1,1, 0) , CH) = (tit, os. ostel og le} = (1,1,02 F (7(t)). Og'(t)= (36, 47,070[110270 {Fodra jst dt = (1+2) = 2 Ly: (1;110) to (ly, i) os valt)= (1, 1, t). (t) = {0, 0,15 FIYLt). F'(t) = (3,4,24).(0,0,13 = gt ff.dr = ['zt dt 22(te) = 1 e o Sescor e f andre 3+1=