16.1.9 Line Integral over space curves

[karush]

Evaluate

$\displaystyle \int_C(x+y)ds$
where C is the straight-line segment
$x=t, y=(1-t), z=0, $
from (0,1,0) to (1,0,0)

ok this is due tuesday but i missed the lecture on it
so kinda clueless.
i am sure it is a easy one.

 

[Alone]

Use $ds = \sqrt{(dx/dt)^2+(dy/dt)^2+(dz/dt)^2}dt$, take derivative of $(x(t),y(t),z(t))$ with respect to t, and then the integral goes from $(x,y,z)=(0,1,0) $ to $(1,0,0)$ check what it means for the t variable.