Question

2. Evaluate the line integral where C is the given curve: BE SURE THAT YOU PARAMETERIZE EACH CURVE! (a) e dr where C is the are of the curve r y' from (-1,-1) to (1, 1): (b) dr dy where C conusists of the arc of the circle 2+ 4 from (2.0) to (0.2) followed by the line segment from (0.2) to (4,3) (c) y': ds where C is the line segment from (3, 1,2) to (1,2.5)+ Fully simplify answer (d) /-(r2 + y2 + H) ds where C, is such that x-t, y-cos 2t. : = sin 2t, 0 t 2n e) vdr y dr + dy + z dz where C is such that r Vi, y t,:2, 1sts4 Fully simplify answer

please be clear as possible. thanks

Answer 1

3 SS gue 5 IS CI cost)Jalt sint Cost 3 巴63 2 Ca

So S2 d osts) 3 3 ds - 2.t囹2. | 11@ sin 992 tecos 3 t)a dt dt つ(T 8n3 3

Ratは 七 So 63 3t2 dt. t' e tsdt = (e-を CI IS) is 2- -t 3 3 dヒ つ(T Br13