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Use the Divergence Theorem to calculate the surface integral {image} {image} S is the surface of the box bounded by the planes x = 0, x = 4, y = 0, y =

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Presentation on theme: "Use the Divergence Theorem to calculate the surface integral {image} {image} S is the surface of the box bounded by the planes x = 0, x = 4, y = 0, y ="— Presentation transcript:

1 Use the Divergence Theorem to calculate the surface integral {image} {image} S is the surface of the box bounded by the planes x = 0, x = 4, y = 0, y = 3, z = 0, z = 5. -360 40 600 1,080 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 the Divergence Theorem to calculate the surface integral {image} {image} S is the surface of the unit ball {image} {image} 1. 2. 3. 4. 5. 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 the Divergence Theorem to calculate the surface integral {image} that is, calculate the flux of F across S. {image} S is the sphere {image} {image} 1. 2. 3. 4. 5. 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 Use the Divergence Theorem to calculate the surface integral {image} that is, calculate the flux of F across S. {image} S is the surface of the solid that lies above the xy-plane and below the surface {image} 25.43 26.85 23.49 18.63 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 {image} Find the flux of F across the part of the paraboloid {image} that lies above the plane z = 1 and is oriented upward. {image} 1. 2. 3. 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


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