Evaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is the sphere given by x^2 + y^2 + z^2 = 9.(a) 120π(b) 180π(c) 240π(d) 300πThis question was addressed to me during a job interview.My enquiry is from Gauss Divergence Theorem topic in division Vector Calculus of Electromagnetic Theory

Evaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is the

1.	Evaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is the sphere given by x^2 + y^2 + z^2 = 9.(a) 120π(b) 180π(c) 240π(d) 300πThis question was addressed to me during a job interview.My enquiry is from Gauss Divergence Theorem topic in division Vector Calculus of Electromagnetic Theory
Answer» Correct answer is (b) 180π To elaborate: 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 4πr^3/3 and r = 3units.Thus we get 180π.

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