Question

If a function is described by F = (3x + z, y^2 − sin x^2z, xz + ye^x5), then the divergence theorem value in the region 0<x<1, 0<y<3 and 0<z<2 will be

(a) 13

(b) 26

(c) 39

(d) 51

I had been asked this question by my college professor while I was bunking the class.

Asked question is from Gauss Divergence Theorem topic in chapter Vector Calculus of Electromagnetic Theory

Answer 1

The correct option is (c) 39

To explain I would say: Div (F) = 3 + 2y + x. By divergence theorem, the triple integral of Div F in the region is ∫∫∫ (3 + 2y + x) dx dy dz. On integrating from x = 0->1, y = 0->3 and z = 0->2, we get 39 units.