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 .

Question

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 .

anonymous · Answer

dr = dxi + dyj + dzk

anonymous · Answer

could explain more clearly? @him1618

anonymous · Answer

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

experimentx · Answer

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

anonymous · Answer

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

experimentx · Answer

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

anonymous · Answer

@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?

experimentx · Answer

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