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F dot dr problems

  1. May 11, 2009 #1
    1. The problem statement, all variables and given/known data

    P = pi

    Evaluate [tex]\int[/tex] F [tex]\cdot[/tex]dr where c is the curve given by r(t) = (t+sin[tex]\pi[/tex]t)i + (2tcos[tex]\pi[/tex]t)j

    F = (4x3y2 - 2xy3) i + (2x4y - 3x2y2 + 4y3)j



    2. Relevant equations



    3. The attempt at a solution

    When I dot them I get an extremely long expression.

    [tex]\int[/tex] 4x3y2t - 4xy3t - 2xy3sinPt + 4x4yt + 2x4cosPt - 6x2y2t - 3x2y2cosPt + 8y3t + 4y3cosPt dt evaluated from t = 0 to to = 1


    2x3y2 - 2xy3 +2Pxy3cosPt + 2x4y + 2Px4ysinPt - 3x2y2 - 3Px2y2sinPt + 4y3 + 4Py3sinPt
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 11, 2009 #2

    quasar987

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    I haven'T checked it you have doted correctly but once that is done, you have to replace all the x in there by t+sin(pi*t) and all the y by 2tcos(pi*t). Then simplify if possible and integrate...
     
  4. May 12, 2009 #3

    Shooting Star

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    Don't even think of doing it directly!

    What is the curl of F? Once you spot that, use Green's theorem or some other property to get the result in one line.
     
  5. May 13, 2009 #4
    Ah hah, Is this right

    [tex]\int[/tex]F dot dr = [tex]\int[/tex]curl F dot dA = 0

    Because

    F = (4x3y2 - 2xy3) i + (2x4y - 3x2y2 + 4y3)j


    curl F = (8x3y - 6xy2 - 8x3y + 6xy2)k = 0
     
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