GATE 2021 MA – Question 22

Calculus · Vector Calculus · 1 mark · Multiple choice

A twice continuously differentiable f:ℝ³→ℝ satisfies div(∇f)=6. On the unit sphere S let n be the unit outward normal. Find ∫_S∇f·n dS.

Show answer and explanation

Correct answer: (D) 8π

Explanation

The divergence theorem gives flux=∫_(unit ball)Δf dV=6×(4π/3)=**8π, D**.

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