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

I Line integral limits

  1. Sep 10, 2016 #1
    I want to the line integral in the following picture:

    P220f03.png

    The field is the blue arrows that go left to right, and the path is the orange line that is going from right to left.

    Just by looking at the picture, it is clear that the result will be negative, but when I set up the integration this is what I get:

    I'm letting the field be:

    [tex]f(x)=\hat{x}[/tex]

    and since the path is pointing left, ds will be:

    [tex]ds=dx*(-\hat{x})=-dx\hat{x}[/tex]

    and the path goes from x=1 to x=0, so the integration limits are from 1 to 0.

    so the line integral is:

    [tex]\int^b_a f \cdot ds=\int^0_1 (\hat{x} \cdot (-dx\hat{x})) = \int^0_1 (-dx) = 1[/tex]

    Why am I getting a positive number?
     
  2. jcsd
  3. Sep 10, 2016 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    You are double counting the negative sign of dx by both inserting it explicitly and letting the integration go from 1 to 0.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Line integral limits
  1. Line integral (Replies: 7)

  2. Line integral (Replies: 1)

  3. Line integral (Replies: 3)

  4. Line Integral (Replies: 11)

  5. Line integrals (Replies: 4)

Loading...