Using Green's theorem evaluate oint_C(6y+x)dx+(y+2x)dy where C is the boundary

Cheyanne Leigh

Cheyanne Leigh

Answered question

2020-11-12

Using Green's theorem evaluate C(6y+x)dx+(y+2x)dy where C is the boundary of the

Answer & Explanation

avortarF

avortarF

Skilled2020-11-13Added 113 answers

Here we have to evalute the integral (6y+x)dx+(y+2x)dy over the regin bounced by y=x2andx=y2 say the regin D.By Greens theorem
(6y+x)dx+(y+2x)dy=D(x(y+2x)y)(6y+x)dydx
01y=x2y=x(x(y+2x)y(6y+x))dydx
=01y=x2y=x(26)dydx
401y=x2y=xdydx
401(xx2)dx
=4x3232x33|01 =4(2313)
=43

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