Question

please calculate directly, my answer is (3/2)pi+32/3 is that correct?

(15%) Evaluate the line integral -r-y + ) dz+ (z+2cy+3)dy, where C consists of the arc Ci of the quarter circle +y 1,x 2 0,y 0, from (0,-1) to (1,0) followed by the arc C2 of the quarter ellipse 4z2y2 - 4, 2 0, y 20, from (1,0) to (0, 2)

Answer 1

Parametric equation of Cı : r(t) cost, sin t), t 2 π Parametric equation of C2: r(t) -cost,2sin t) , 0 s IFcF-F r(o)t-cos-sint+ i+(cost +2 sin rcost+3)-sin t.cost)dr -sn t.costidt 3a12 Sin t -cost-sin t(cos2 -sin t 2sin tcost +3)cost dt 3a12 sint sin tcost+1+2sin tcos t3cost dt 3/2 in t -cost-sin t_ i(cost4sin tcost+3)-sint,2costy dt -sin t-cost-2 sin t +2sintcost4 sin tcos t 3 2cost ldt =1 2 sin tcost-2sint+2 +8sin tcos t+6cos t ldt 2 25 Therefore, 25 3r 19

C2 4x84 0.-I