Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I How do we compute an integral with a dot product inside ?

  1. Dec 30, 2016 #1
    I was trying to solve a problem involving work , as we know :
    [tex] w = \int_{a}^{b} \vec{f}.d\vec{s} [/tex]

    but in my problem the path was cyrcular , so how to evaluate this kind of integral ? 9.PNG
    Last edited: Dec 30, 2016
  2. jcsd
  3. Dec 30, 2016 #2
    You have to evaluate the dot product first.
  4. Dec 30, 2016 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    First of all, this is math. Secondly, it is hard to know exactly why are you are not able to do this, because presumably, you should know how to do a line integral by the time you are taking such a course. You also didn't provide sufficient information of the problem.

    Assuming that this a "circular" path, and that your origin is at the center of this circular path, then ds is simply the line element of the circle, i.e.

    ds = r dθ θ

    where θ is the unit vector in the angular direction. Refer to the figure below.

    line element.jpg
    Then your integral limits will be the angles of the two end points.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted