The GATE Grind

GATE 2022 EE – Question 52

Engineering Mathematics · Calculus: Vector identities, Directional derivatives, Line integral, Surface integral, Volume integral, Stokes's theorem, Gauss's theorem, Divergence theorem, Green's theorem · 2 marks · Multiple choice

Let $\vec E(x,y,z)=2x\hat\imath+5y\hat\jmath+3z\hat k$. The value of $\iiint_V(\vec\nabla\cdot\vec E)\,dV$, where $V$ is the volume enclosed by the unit cube defined by $0\le x\le1,\ 0\le y\le1,\ and\ 0\le z\le1$, is

  1. 3
  2. 8
  3. 10
  4. 5

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) 10

Explanation

$\nabla\cdot\vec E=2+5+3=10$, a constant, so the integral over the unit cube is $10\times1=10$.