Results 1 to 4 of 4

Math Help - Line integral

  1. #1
    Newbie
    Joined
    Apr 2007
    Posts
    2

    Line integral

    Show that the line integral is independent of path and evaluate the integral.
    c (1-ye^(-x)dx + e^(-x)dy)
    C (suppost to be a subscript to the integral) is any path from (0,1) to (1,2)

    To prove it is independent of path, i did:
    dP/dy = (1-ye^(-x))dy = -e^(-x)
    dQ/dx = (e^(-x))dx = -e^(-x)
    So, since they are the same, it is conservative, which means it is independent of path.

    I'm having some trouble evaluating the integral. I think i do:
    c (F * dr) = f(1,2)-f(0,1)

    = (1-(2)e^(-1)) + e^(-1)) - (1-e^(0) + e^(0))
    =1 - 2e^(-1) + e^(-1) - 1
    = -2e^(-1) + e^(-1)
    = -e^(-1)

    I don't think that is correct. I thought is was suppost to equal zero.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,394
    Thanks
    1479
    Awards
    1
    The primitive function is f(x,y)=x+ye^{-x}.
    That is what is used to evaluate the integral.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2007
    Posts
    2
    so,
    f(x,y) = x + ye^(-x)
    f(1,2)-f(0,1) = 1+2e^(-1)-1 = 2e^(-1)

    Is that correct? How did you get the primitive function?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,394
    Thanks
    1479
    Awards
    1
    Quote Originally Posted by justme3 View Post
    so,
    f(x,y) = x + ye^(-x)
    f(1,2)-f(0,1) = 1+2e^(-1)-1 = 2e^(-1)

    Is that correct? YES
    Quote Originally Posted by justme3 View Post
    How did you get the primitive function?
    I just looked at the F function and saw what primitive, f, gives F when that partials are found.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 11th 2011, 11:30 PM
  2. [SOLVED] Line Integral along a straight line.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 11th 2011, 07:18 PM
  3. Replies: 0
    Last Post: May 9th 2010, 01:52 PM
  4. [SOLVED] Line integral, Cauchy's integral formula
    Posted in the Differential Geometry Forum
    Replies: 7
    Last Post: September 16th 2009, 11:50 AM
  5. [SOLVED] Line integral, Cauchy's integral formula
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: September 15th 2009, 01:28 PM

Search Tags


/mathhelpforum @mathhelpforum