Use Green's Theorem to evaluate oint_C(x^2+y)dx-(3x+y^3)dy Where c is the ellipse x^2+4y^2=4

aortiH 2021-02-21 Answered
Use Greens
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Expert Answer

wheezym
Answered 2021-02-22 Author has 103 answers

Step 1
It is required to calculate the value of the integral using green’s theorem:
C(x2+y)dx(3xy3)dy where c is ellipse x2+4y2=4
Step 2
CPdx+Qdy=R(QxPy)dA
Step 3
So,
C(x2+y)dx(3x+y3)dy=Rx((3x+y3))y(x2+y)
=R(31)dA
=R(4)dA
Step 4
C(x2+y)dx(3x+y3)dy=R(4)dA=1122(4)dxdy
=(4)11[x]22dy
=(4)11(2(2))dy
=(4)114dy
=(16)(y)11
=16(1(1))
=16(2)
C(x2+y)dx(3x+y3)dy=32

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