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F dot dr problems

  • Thread starter joemama69
  • Start date
  • #1
399
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Homework Statement



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



Homework Equations





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

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
quasar987
Science Advisor
Homework Helper
Gold Member
4,773
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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...
 
  • #3
Shooting Star
Homework Helper
1,977
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F = (4x3y2 - 2xy3) i + (2x4y - 3x2y2 + 4y3)j
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.
 
  • #4
399
0
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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