Use Green 's Theorem to evaluate the line integral Orient the curve counterclockwise unless otherwse indicated ( oint C mathbf F cdot d mathbf r ), where ( mathbf F (x, y) left langle x 2 , x 2 ightangle ) and (C ) consists of the arcs (y x 2 ) and (y x ) for (0 leq x leq 1 ) THEOREM 1 Green's Theo...

By Greens Theorem IintC mathbfF cdot d mathbfriintmathcalDleft ...

Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwse indicated. (oint_{C} mathbf{F}

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Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwse indicated.

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$\oint_{C} \mathbf{F} \cdot d \mathbf{r}$, where $\mathbf{F}(x, y)=\left\langle x^{2}, x^{2}ightangle$ and $C$ consists of the arcs $y=x^{2}$ and $y=x$ for $0 \leq x \leq 1$

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Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwse indicated. $\oint_{C} \mathbf{F} \cdot d \mathbf{r}$, where \(\mathbf{F}(x, y)=\left\langle x+y,...
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Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwse indicated. (oint_{C} mathbf{F}

Question:

THEOREM 1 Green's Theorem Let D be a domain whose boundary 3D is a simple closed curve, oriented counterclockwise. If F and F have continuous partial deriva- tives in an open region containing D, then $o F1 dx + F2 dy 1 (F2-F) da dA = ay 2

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Calculus

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