1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Confused about the different types of line integrals

  1. Feb 10, 2006 #1
    what's the difference between
    [tex]\int_{a}^{b} f(r(t)) dt[/tex]
    [tex]\int_{a}^{b} F(r(t)) (dr/dt)dt[/tex]?
    (where F is a vector function)

    because when i'm calculating those two types of questions, the first question just uses dt to integrate the line integral but in the 2nd question, i have to differentiate dr???
  2. jcsd
  3. Feb 10, 2006 #2
    What is r though? Doesn't r have a fairly standard definition ( if we're talking about the vector) as r = (x, y, z) = (x(t), y(t), z(t)) the dr is (dx, dy, dz) Maybe I;ve got it wrong but its late so I apologize if this isn't correct, but they at least SEEM to be more or less the same thing.
  4. Feb 10, 2006 #3
    From what I know, I would say that the second integral is supposed to be evaluated with respect to t. A more conventional way of writing the second integral is:

    \int\limits_a^c {F\left( {r\left( t \right)} \right)} \bullet r'\left( t \right)dt

    Assuming that F and r are vector functions of t. That representation should clear up some confusion. Also, the (dr/dt) or r'(t) is essentially just some vector. So when it is 'dotted' with F(r(t)), which is another vector, your integrand is just a scalar function.
  5. Feb 11, 2006 #4
    i think that the 1st "f" is only a scalar function...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook