Find the value of divergence theorem for the field D = 2xy i + x^2 j for the rectangular parallelepiped given by x = 0 and 1, y = 0 and 2, z = 0 and 3.(a) 10(b) 12(c) 14(d) 16This question was addressed to me in a job interview.Question is from Surface Integral topic in portion Vector Calculus of Electromagnetic Theory

Find the value of divergence theorem for the field D = 2xy i + x^2 j f

1.	Find the value of divergence theorem for the field D = 2xy i + x^2 j for the rectangular parallelepiped given by x = 0 and 1, y = 0 and 2, z = 0 and 3.(a) 10(b) 12(c) 14(d) 16This question was addressed to me in a job interview.Question is from Surface Integral topic in portion Vector Calculus of Electromagnetic Theory
Answer» Correct option is (b) 12 To explain I WOULD say: While evaluating SURFACE INTEGRAL, there has to be two variables and one constant compulsorily. ∫∫D.ds = ∫∫Dx=0 DY dz + ∫∫Dx=1 dy dz + ∫∫Dy=0 dx dz + ∫∫Dy=2 dx dz + ∫∫Dz=0 dy dx + ∫∫Dz=3 dy dx. Put D in equation, the integral value we get is 12.

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