## anonymous one year ago evaluate line integral of (x+y) ds where C is the straight-line segment x=t, y=(1-t), z=0, from (0,1,0) to (1,0,0)

1. Loser66

From (0, 1,0) to (1, 0,0) . That is when t =0 , x = 0, y =1, z =0; when t =1 , x =1, y =0, z=0 Hence, $$0\leq t\leq 1$$ Now the integral: (x +y) w.r.t t is x+y = t +1-t =1 Jacobian: $$\sqrt{(dx/dt)^2+(dy/dt)^2+(dz/dt)^2}dt$$ $$= \sqrt{(1)^2+(1)^2+(0)^2}dt =\sqrt{2}dt$$ Combine all $\int_0^1 \sqrt{2}dt$ I think you can handle it from here.

2. anonymous

thanks