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rohitBegginer

Asked: August 27, 20242024-08-27T15:38:18+05:30 2024-08-27T15:38:18+05:30In: Education

Evaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is the sphere given by x2 + y2 + z2 = 9.

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prasanjit Teacher
2024-09-21T16:05:04+05:30Added an answer on September 21, 2024 at 4:05 pm
Answer: b
Explanation: 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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