## mymathcourses 3 years ago Suppose C is any curve from( 0,0,0) to (1,1,1) and F(x,y,z)=(5z+5y)i+(2z+5x)j+(2y+5x)k . Compute the line integral ∫Fdr .

1. him1618

dr = dxi + dyj + dzk

2. mymathcourses

could explain more clearly? @him1618

3. him1618

you know dr, and you know F..can u tell me the expression for F.dr?

4. experimentX

it might depend on your path ... what path do you choose to take?

5. henpen

It doesn't depend on the path as the curl=0

6. experimentX

then you can choose any path. easiest one ... choose a straight line parametric form of line is r(t) = (0,0,0) + t(1,1,1) ... change all x,y,z in F into this parametric form. i.e. = t,t,t ... integrate it wrt dt ... from 0 to 1

7. mymathcourses

@experimentX but it is said for any curve, thats why i dont know how to solve this problem, not a straight line or sth else, just for any?

8. experimentX

as henpen said earlier, take a curl, if the curl is zero, then the line integral does not depend on path. choose any path.