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 \(0 \leq x \leq 1\)

Transcribed Image Text:

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