Results 1 to 6 of 6
Like Tree1Thanks
  • 1 Post By Prove It

Math Help - Line integral help

  1. #1
    Super Member
    Joined
    Sep 2008
    Posts
    607

    Line integral help

    am stuck on the integration part, so far I have
    x = cost , y = sint

    dx = -sint dt dy = cost dt


     \int ( xy^{2}) dx + ( x^{2}y + 2x) dy subbing in the values for x,y, dx and dy

    i get


     \int^{2\pi}_{0}  ( -cost sin^{3}t + cos^{3}t sint + 2cos^{2}t ) dt

    how do I simply / integrate this expression ?
    Attached Thumbnails Attached Thumbnails Line integral help-screen-shot-2014-06-14-15.23.15.png  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,547
    Thanks
    1418

    Re: Line integral help

    You can integrate the first two terms using substitutions, and the third using a double angle identity.
    Thanks from Tweety
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466

    Re: Line integral help

    I am puzzled by this. The given problem, to integrate x^2ydx+ (x^2y+ 2x)dy, I presume around the unit circle, is not difficult but it is a typical "Calculus III" or "Calculus of several variables" problem while the part you are stuck on is standard "Calculus I". You need a review! Go back to your Calculus I text and look at the chapter on trig integrals.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,547
    Thanks
    1418

    Re: Line integral help

    Have you gotten an answer for this yet? Have you tried using Green's Theorem yet?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Sep 2008
    Posts
    607

    Re: Line integral help

    Yes

     (\frac{1}{4} sin^{4}t )^{2\pi}_{0}  + \frac{1}{4}cos^{4}t)^{2\pi}_{0} + 2 [ \frac{1}{4} sint2t +\frac{t}{2} )^{2\pi}_{0}

    =  2\pi
    using green's theorem i get same
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,547
    Thanks
    1418

    Re: Line integral help

    Be VERY careful with your signs. You have sign errors in the first two terms...
    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