Hello

find the line integral $\displaystyle \int_C ydx+zdy+xdz$

where C consist of line segement C1 from A(2,0,0) to B(3,4,5) followed by C2 from B(3,4,5) to C(3,4,0)

It is not hard I know.

Lets focus on C1:

By finding the parametric equations for this line, we will get:

$\displaystyle x=2+t$

$\displaystyle y=4t$

$\displaystyle z=5t$

Now, finding dx, dz .. etc and substitute them in the integral, easy.

But the problem how did we know that t is from 0 to 1 ???!