Suppose C is any curve from (0,0,0) to (1,1,1) and F(x,y,z) = (5z+4y)i + (4z+4x)j + (4y+5x)k. Compute the line integral F*dr Thanks

Question

Suppose C is any curve from (0,0,0) to (1,1,1) and F(x,y,z) = (5z+4y)i + (4z+4x)j + (4y+5x)k. Compute the line integral  F*dr Thanks

amistre64 · Answer

since the path is irrelevant, wouldnt making it a line be simple?

amistre64 · Answer

r = r' = <1,1,1>

amistre64 · Answer

F(x,y,z) = (5t+4t)i + (4t+4t)j + (4t+5t)k

 F(r(t)) = 9t i + 8t j + 9t k
F*r' = 26t

amistre64 · Answer

$$\int_{0}^{1}26t~dt=13$$

anonymous · Answer

I don't think that is right. Does it sound right to do something like find ∇f for each i,j, and k and then combine them?

amistre64 · Answer

anonymous · Answer

I just did it that with gradients and I got the same answer as you did. Thanks

amistre64 · Answer

YAY!! :)

amistre64 · Answer