Solved: Evaluating F dot dr Integral for P = pi

  • Thread starter Thread starter joemama69
  • Start date Start date
  • Tags Tags
    Dot
joemama69
Messages
390
Reaction score
0

Homework Statement



P = pi

Evaluate \int F \cdotdr where c is the curve given by r(t) = (t+sin\pit)i + (2tcos\pit)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.

\int 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
 
Physics news on Phys.org
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...
 
joemama69 said:
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.
 
Ah hah, Is this right

\intF dot dr = \intcurl F dot dA = 0

Because

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


curl F = (8x3y - 6xy2 - 8x3y + 6xy2)k = 0
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

Similar threads

Back
Top