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Evaluate the surface integral fr-ds, where r is the position vector, over that part of the surface z = a²-x²-y² for which z ≥ 0, by each of the following methods. (a) Parameterise the surface as x = a sin cos , y = a sin 0 sin o, z = a² cos² 0, and show that r. ds = a¹ (2 sin³ 0 cos 0 +cos³0 sin 0) d0 do. (b) Apply the divergence theorem to the volume bounded by the surface and the plane z = 0.

Evaluate the surface integral fr-ds, where r is the position vector, over that part of the surface z = a²-x²-y² for which z ≥ 0, by each of the following methods. (a) Parameterise the surface as x = a sin cos , y = a sin 0 sin o, z = a² cos² 0, and show that r. ds = a¹ (2 sin³ 0 cos 0 +cos³0 sin 0) d0 do. (b) Apply the divergence theorem to the volume bounded by the surface and the plane z = 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Evaluate the surface integral fr.ds, where r is the position vector, over that part of the surface z = a²-x² - y² for which z ≥ 0, by each of the following methods. (a) Parameterise the surface as x = a sin 0 cos , y = a sin 0 sin o, z = a² cos² 0, and show that r. ds = a^(2 sin³ 0 cos 0 +cos³ 0 sin 0) do do. (b) Apply the divergence theorem to the volume bounded by the surface and the plane z = 0.
Transcribed Image Text:Evaluate the surface integral fr.ds, where r is the position vector, over that part of the surface z = a²-x² - y² for which z ≥ 0, by each of the following methods. (a) Parameterise the surface as x = a sin 0 cos , y = a sin 0 sin o, z = a² cos² 0, and show that r. ds = a^(2 sin³ 0 cos 0 +cos³ 0 sin 0) do do. (b) Apply the divergence theorem to the volume bounded by the surface and the plane z = 0.
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