Use Green's Theorem to find int_C vec(F) * d vec(r) where vec(F) = <<y^3, - x^3>> and C is the circle x^2+y^2=3.

Jaya Legge 2020-11-08 Answered
Use Green's Theorem to find CFdr where F=y3,x3 and C is the circle x2+y2=3.
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Expert Answer

comentezq
Answered 2020-11-09 Author has 106 answers

Step 1
The given vector is
F=y3ix3j
Step 2
I=CFdr
but d r=dxi^+dyj^
I=C(y3i^x3j^).(dxi^+dyj^)
=C(y3dxx3dy)
The given circle
x2+y2=3
x2+y2=(3)2
radius=3
Apply Green Theorem
C(Mdx+Ndy)=(NxDelMy)dxdy
I=(3x23y2)dxdy
=3(x2+y2)dxdy
=3(x2+y2)dxdy
=9dxdyx2+y2=3
=9x Area of circle
=9xπr2
=9xπx(3)2
I=27π

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