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From: Stephen Montgomery-Smith on 1 May 2010 14:33
Stephen Montgomery-Smith wrote:
> aegis wrote:
>> I have the line integral y - ln(x^2 + y^2)dx + 2arctan(y/x)dy where C
>> is the ellipse: [(x-1)^2]/9 + [(y+2)^2]/4 = 1
>>
>> Applying green's theorem, it boils down to the iterated integral
>> int( int( -1 ) ) dA, however, how should this be evaluated in
>> terms of C?
>>
>> --
>> aegis
>
>
> I think this question is harder than perhaps even the creator of the
> question intended. You cannot use Green's Theorem when the functions are
> discontinuous in the domain. Fortunately, (0,0) is not contained on the

I meant "in" not "on".

> ellipse, so no problems with ln(x^2+y^2). However the ellipse does
> contain two points where x=0. Using the usual conventional meaning of
> arctangent (remember tan x = y has many solutions x for a given y),
> arctan(y/x) will be discontinuous at those two points. This makes the
> problem quite a bit harder.
>

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