Question

Value of a line integral

Answer 1

\[\int\limits_{a}^{b}c dx\]\[=c(b-a)\]

Answer 2

If\[\vec F(r) d \vec r<0, vec r=\vec r(t) \] for all t, is it \[\int\limits_{C} \vec F(r) d \vec r<0\]?

Answer 3

\[\vec r=\vec r(t)\]

Answer 4

what's vecr? you mean vector?

Answer 5

yes, I made mistake in typing, I corrected myself below

Answer 6

actually I'm not really good when it come to vectors, so I don't think I understand he question properly, though assume your question missing one term of the integral.
then I'll assume it's some other constant D okay?

Answer 7

I made a huge mistake.
\[\vec F_v=-k \dot{\vec r}, \dot{\vec r}=\frac{d \vec r}{dt}\]
\[\vec F_v d \vec r<0\]
I need to know the value of \[\int\limits_{C} \vec F_v d \vec r\]

Answer 8

k is positive constant

Answer 9

there's no upper term for the integral?!

Answer 10

It's closed integral on closed curve C

Answer 11

okay I'm really sorry, either I don't think I understand the question , or the value is clearly 0 since the bounds are similar, I wish I could be more convenient :(

Answer 12

What's the curve? @gorica

Answer 13

what do you mean what's the curve?

Answer 14

This is a line integral over the curve \(C\), isn't it? What is \(C\)?

Answer 15

You mean if C is a circle, ellipse,...? I don't really understand your question. If you ask about the shape of C, it's not defined. It's an arbitrary closed curve. The shape doesn't matter.