377. Evaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is the sphere given by x2 + y2 + z2 = 9.
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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 sRead more
b
See lessExplanation: 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.
Answer: 180π 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 voluRead more
Answer: 180π
See lessExplanation: 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.
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 volumeRead more
Answer: b
See lessExplanation: 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.
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 theRead more
b)
See lessExplanation: 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.