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Evaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is the sphere given by x2 + y2 + z2 = 9.
  • a)
    120π
  • b)
    180π
  • c)
    240π
  • d)
    300π
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Evaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is...
We cannot evaluate the surface integral without knowing what surface and what function we are integrating over. Please provide more information.
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Evaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is...
We could parameterise surface and find surface integral, but it is wise to use divergence theorem to get faster results. The divergence theorem is given by ∫∫ F.dS = ∫∫∫ Div (F).dV
Div (3x i + 2y j) = 3 + 2 = 5.
Now the volume integral will be ∫∫∫ 5.dV, where dV is the volume of the sphere 4πr3/3 and r = 3units.
Thus we get 180π.
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Evaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is the sphere given by x2+ y2+ z2= 9.a)120πb)180πc)240πd)300πCorrect answer is option 'B'. Can you explain this answer?
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