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Engineering Mathematics
Calculus
GATE 2018
Medium

The value of the integral ∯ₛ r⃗·n⃗ dS over the closed surface S bounding a volume V, where r⃗ = x î + y ĵ + z k̂ is the position vector and n⃗ is the normal to the surface S, is

  • AV
  • B2V
  • 3V
  • D4V

Explanation

By the divergence theorem, ∯ₛ r⃗·n⃗ dS = ∭ᵥ div(r⃗) dV. div(r⃗) = ∂x/∂x+∂y/∂y+∂z/∂z = 3 (constant), so the integral = 3V.

Source: GATE ME 2018 Session 1 (Set 1) (2018)

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