Using Green's Theorem, the line integral $\int $C $2 x y d x - x ^ { 2 } y d y$ where C is the triangle with vertices at (0, 0), (1, 0), and (1, 1), is

A) $- \frac { 5 } { 12 }$
B) $- \frac { 11 } { 12 }$
C) $- 1$
D) $\frac { 4 } { 15 }$
E) $- \frac { \pi } { 2 }$

Question

Using Green's Theorem, the line integral $\int $C $2 x y d x - x ^ { 2 } y d y$ where C is the triangle with vertices at (0, 0), (1, 0), and (1, 1), is

A) $- \frac { 5 } { 12 }$
B) $- \frac { 11 } { 12 }$
C) $- 1$
D) $\frac { 4 } { 15 }$
E) $- \frac { \pi } { 2 }$

Quizplus · Accepted Answer

Using Green's Theorem, the line integral becomes the area of the triangle, which is $\frac{1}{2} \times 1 \times 1 = \frac{1}{2}$.

Using Green's Theorem, the Line Integral ∫\int ∫ C 2xydx−x2ydy2 x y d x - x ^ { 2 } y d y2xydx−x2ydy

Using Green's Theorem, the Line Integral $\int$ C $2 x y d x - x ^ { 2 } y d y$