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nestleeng

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## Homework Statement

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.

## Homework Equations

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Divergence theorem, although on the RHS I put vector DS = nDS.

## The Attempt at a Solution

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.

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