Use Green's Theorem to evaluate the double integral

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Presentation transcript:

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

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 = 16. 8,192 -3,968 -7,936 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

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

A particle starts at the point (-2, 0),moves along the x - axis to (2, 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