I need help with this problem. The problem is attached.

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- Dec 9th 2009, 03:07 PMmeks08999Green's Theorem
I need help with this problem. The problem is attached.

- Dec 9th 2009, 03:29 PMJester
From Green's theorem

$\displaystyle

\int \limits_C -y^3\,dx +(x^3+2x+y)\,dy = \iint \limits_R 3x^2+2+3y^2\,dA

$

and since

$\displaystyle 3x^2 + 2 +3y^2 > 0$,

then

$\displaystyle \iint \limits_R \left(3x^2 + 2 +3y^2 \right) dA > 0\;\; \Rightarrow\;\; \int \limits_C -y^3\,dx +(x^3+2x+y)\,dy > 0$ .