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krati jain
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Asked: 2023-05-22T15:46:59+00:00 In:

384. For a function given by F = 4x i + 7y j +z k, the divergence theorem evaluates to which of the values given, if the surface considered is a cone of radius 1/2π m and height 4π2 m. a) 1 b) 2 c) 3

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384. For a function given by F = 4x i + 7y j +z k, the divergence theorem evaluates to which of the values given, if the surface considered is a cone of radius 1/2π m and height 4π2 m. a) 1 b) 2 c) 3
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    1. Answer: b
      Explanation: Div (F) = 4 + 7 + 1 = 12. The divergence theorem gives ∫∫∫(12).dV, where
      dV is the volume of the cone πr3h/3, where r = 1/2π m and h = 4π2 m. On substituting the
      radius and height in the triple integral, we get 2 units.

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    3. Answer: b
      Explanation: Div (F) = 4 + 7 + 1 = 12. The divergence theorem gives ∫∫∫(12).dV, where
      dV is the volume of the cone πr3h/3, where r = 1/2π m and h = 4π2 m. On substituting the
      radius and height in the triple integral, we get 2 units.

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    4. Answer: b
      Explanation: Div (F) = 4 + 7 + 1 = 12. The divergence theorem gives ∫∫∫(12).dV, where
      dV is the volume of the cone πr3h/3, where r = 1/2π m and h = 4π2 m. On substituting the
      radius and height in the triple integral, we get 2 units.

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    6. Answer: b
      Explanation: Div (F) = 4 + 7 + 1 = 12. The divergence theorem gives ∫∫∫(12).dV, where
      dV is the volume of the cone πr3h/3, where r = 1/2π m and h = 4π2 m. On substituting the
      radius and height in the triple integral, we get 2 units.

      • 0

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