Q.26 Let S, be the hemisphere x? + y? + z? = 1, z > 0 and S2 be the closed disc x? + y? <1 in the xy-plane. Using Gauss' divergence theorem, evaluate || F.d5 where F = z?xỉ +( + tanz)j + (x²z +y²) k and S = S,US2. Also evaluate the 3 integral F.dS.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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Q.26
Let S be the hemisphere x? + y? + z? = 1, z > 0 and S, be the closed disc
x² + y? <1 in the xy-plane. Using Gauss' divergence theorem, evaluate
|| F.d5
where F = z?xỉ + (-
+ tanz)j + (x²z + y²) k and S = S,US,. Also evaluate the
3
I| F.a5.
integral
Transcribed Image Text:Q.26 Let S be the hemisphere x? + y? + z? = 1, z > 0 and S, be the closed disc x² + y? <1 in the xy-plane. Using Gauss' divergence theorem, evaluate || F.d5 where F = z?xỉ + (- + tanz)j + (x²z + y²) k and S = S,US,. Also evaluate the 3 I| F.a5. integral
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