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posted by  Joedd on 5/20/2008 2:34:12 AM  |  status: Live  

Line integral

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Question Details:
Let C be the upper half of the circle x2+y2 = 2ax, y0 oriented counterclockwise.
Calculate the line integral .
 
Please write down step by step!

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posted by WSAN on 5/22/2008 6:29:39 AM  |  status: Live
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by green's theorem, we have
p = exsiny -2y , q = excosy - 2 ,
lwhere  the surface is the semicircle with radisu a and centre (a,o).
∴= 2 (area of the semi circle) =
SWAN
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posted by Joedd on 5/22/2008 7:12:24 AM  |  status: Live
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 = πa2
 
Your answer is wrong!
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posted by Bernard on 5/22/2008 7:43:57 AM  |  status: Live
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Response Details:
The first part is correct, the second part is a mess.
You have to calculate (after application of Greene)
. The region R enclosed by C is half a circle with radius a:

This means that the integral over the area only gives you the area of half of the circle times two:
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posted by Puksa on 5/22/2008 8:06:09 AM  |  status: Live
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Joedd's comment:
"Thank you for answering this question! Actually, I prefer the first one. "
Response Details:
Well without green is easier I think:
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