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: Proving a theorem in line integrals

  1. Feb 13, 2016 #1
    At the bottom of the picture, I couldn't understand why differentiating with respect to x gives the first integral at the right-hand side 0. Thanks for reading.
     

    Attached Files:

  2. jcsd
  3. Feb 13, 2016 #2

    HallsofIvy

    User Avatar
    Science Advisor

    In my opinion, that is simply wrong. Rather than taking [itex]C_1[/itex] to be "any path from (a, b) to [itex](x_1, y)[/itex]" we must choose [itex]C_1[/itex] to be the vertical line from (a, b) to [itex](a, y)[/itex] then take [itex]C_2[/itex] to be the horizontal line from [itex](a, y)[/itex] to [itex](x, y)[/itex].
     
  4. Feb 13, 2016 #3
    I'm no math pro, but my guess would be that since you have the hypothesis that your integral is path independent, then
    [tex]
    \int_{C_1} F\cdot dr = \int^{(x1,y)}_{(a,b)} F\cdot dr = f(x1,y) - f(a,b)
    [/tex]
    which differentiated w.r.t. x gives 0 and w.r.t. y does not (since the point (x,y) is arbitrary, y is arbitrary but x1,a,b are fixed)
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Loading...