1. Use Green's Theorem to evaluate the double integral
Use Green's Theorem to evaluate the double integral. {image} C is a triangle with the vertices (0,0), (3,0) and (3, 3). Select the correct answer. The choices are rounded to the nearest hundredth.
{image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. Use Green's Theorem to evaluate the line integral along the given positively oriented curve. {image} and C is the boundary of the region enclosed by the parabola {image} and the line y = 49.
-200,312
-100,156
201,684 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. Use Green's Theorem to evaluate the line integral along the given positively oriented curve. {image} and C is the boundary of the region between the circles {image} . Choose the correct answer.
{image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. A particle starts at the point (-1, 0),moves along the x - axis to (1, 0) and then along the semicircle {image} to the starting point. Use Green's Theorem to find the work done on this particle by the force field {image} Choose the correct answer.
{image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. Let D be a region bounded by a simple closed path C in the xy
Let D be a region bounded by a simple closed path C in the xy. Then the coordinates of the centroid {image} of D are {image} where A is the area of D. Find the centroid of the triangle with vertices (0, 0); (1, 0) and (0, 1). Choose the correct answer.
{image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50