The surface integral _s 1/π ≤ft( 9xi - 3yj ) .nds over the sphere given by x² + y² + z² = 9 is - General SHORT_ANSWER PYQs Based Test - 09 : Line, Surface, and Volume Integrals | ExamTest.live

mediumSHORT_ANSWERPYQs Based Test - 09 : Line, Surface, and Volume IntegralsGeneral

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The surface integral \int s \int \frac{1}{π} (9 x i - 3 y j) .nds over the sphere given by x² + y² + z² = 9 is

Correct Answer

Solution & Step-by-step Explanation

In the range: 216 - 216 By Gauss divergence theorem s \int \overset{ˉ}{F} . \overset{n}{ˉ} d s = v \int d i v \overset{ˉ}{F} d v Here div F̅ = 9 - 3 =6 ∴ \int s \int \frac{1}{π} (9 x \overset{ˉ}{i} - 3 y \overset{ˉ}{j}) . \overset{n}{ˉ} d s = \frac{1}{π} v \int 6 d v = \frac{1}{π} 6 v = \frac{1}{π} 6 (\frac{4}{3} π r^{3}) = 8(3)³ = 216

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The surface integral \int s \int \frac{1}{π} (9 x i - 3 y j) .nds over the sphere given by x² + y² + z² = 9 is