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Verify Divergence Theorem for V = xy i − y^2 j + z k and Enclosed Surface
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[QUOTE="nestleeng, post: 5346969, member: 580177"] [h2]Homework Statement [/h2] Verify the divergence theorem for the function V = xy i − y^2 j + z k and the surface enclosed by the three parts (i) z = 0, s < 1, s^2 = x^2 + y^2, (ii) s = 1, 0 ≤ z ≤ 1 and (iii) z^2 = a^2 + (1 − a^2)s^2, 1 ≤ z ≤ a, a > 1. [h2]Homework Equations[/h2] [/B] [ATTACH=full]184187[/ATTACH][ATTACH=full]184188[/ATTACH][PLAIN][PLAIN]https://upload.wikimedia.org/math/7/b/7/7b759968274f2f43cfaab3ce5672da74.png[PLAIN]https://upload.wikimedia.org/math/a/b/9/ab9fd5a4aaa36e402c98cbd36af3a70d.png[/PLAIN] Divergence theorem, although on the RHS I put vector DS = nDS. [h2]The Attempt at a Solution[/h2] So I solved the LHS and got the answer to be a*Pi on the RHS, splitting the 3 surfaces, (i) got 0 for integral (ii) got 0 for integral (iii) staying in cartesians, I have to integrate ((1-a^2)(-x^2 y +y^3 + x^2 +y^2) +a^2)/Sqrt(a^2+(1-a^2)(x^2+y^2) dxdy between -1 and 1 for x and y which even Wolfram can't do. Spent hours on this please help. [/QUOTE]
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Verify Divergence Theorem for V = xy i − y^2 j + z k and Enclosed Surface
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