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Green sentence

  1. Sep 13, 2004 #1

    ori

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    we define C as the border of the area
    D={(x,y)|(x^2+y^2)^2<=x^2-y^2,x>=0}
    whats the value of the integral
    S(x^2y^3+2y)dx+(x^3y^2+3x)dy
    C
    while C is against the clock direction

    it's the possitive direction,
    the field components are from C1 (continious and devertive continious)
    the area connected and muzzled
    so i tried to used grin sentence and got:
    SSdQ/dx-dP/dy
    D

    SS1dxdy
    D

    trans to D*:
    x=rcost
    y=rsint
    therefore j=r

    i assigned that at to D to get new D*
    r^4<=r^2(cos^2(t)-sin^2(t))
    r^2<=[1+cos(2t)]/2 - [1-cos(2t)]/2
    r^2<=cos(2t)
    0<=r<=sqrt(cos(2t))

    also
    x>=0 therefore
    rcost>=0
    cost>=0
    -pi/2<=t<=pi/2

    so our integral is
    SSr dr dt
    D*

    S [r^2/2] dt
    (1/2)S cos(2t) dt
    (1/2) [sin(2t)/2]
    (1/4) (0+0 )
    0

    the right answer is 1/2

    where's my mistake?
    thanks
     
  2. jcsd
  3. Sep 13, 2004 #2

    ori

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  4. Sep 15, 2004 #3

    ori

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    i found my mistake at the ingeral just how i choose the shape plz?
     
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