Question 1
Use Green's Theorem to evaluate the line integral
![](data:image/png;base64, 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)
counterclockwise around the square with vertices (0, 3), (3, 0), (-3, 0), and (0, -3).
◦ 18
◦ 0
◦ 180
◦ 36
◦ -36
Question 2
Evaluate the integral
![](data:image/png;base64, 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)
(x
2) - 2y) dx + (3x - ysin(y
2)) dy counterclockwise around the triangle in the xy-plane having vertices (0, 0), (2, 2), and (2, 0).
◦ 10
◦ 20
◦ 2
◦ 0
◦ 5