Apply Green's Theorem to evaluate the integral.
-$$\oint _ { C } ( 6 y d x + 8 y d y )$$
$C$ : The boundary of $0 \leq x \leq \pi , 0 \leq y \leq \sin x$
A) 4
B) 2
C) 0
D) -4

Question

Quizplus · Accepted Answer

Using Green's Theorem, the integral becomes$$\oint _ { C } ( 6 y d x + 8 y d y ) = \iint _ { R } ( 8 - 6 ) d A = 2 \iint _ { R } d A = 2 \cdot 	ext{Area}(R) = 2 \cdot \frac{\pi^2}{2} = \pi^2$$

Apply Green's Theorem to Evaluate the Integral ∮C(6ydx+8ydy)\oint _ { C } ( 6 y d x + 8 y d y )∮C​(6ydx+8ydy)

Apply Green's Theorem to Evaluate the Integral $\oint _ { C } ( 6 y d x + 8 y d y )$