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

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  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

    ZapperZ

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    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.

    Zz.
     
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