S let d be the region enclosed by the curve c and it

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Unformatted text preview: osed curve C for which the value of the line integral 3 ( −3 ) − 3 C is a maximum and determine this maximum value. S Let D be the region enclosed by the curve C and it follows from Green’s theorem that ( C 3 −3 ) − 3 = ((− 3 ) −( 3 D −3 ) ) =3 (1 − D 6 2 − 2 ) From this we see easily that the line integral is maximized if the region D is given by 2 + 2 ≤ 1, which is the unit disk and hence C is the unit circle positively oriented. In this case, the maximum value is 2π 3 (1 − 2 + 2 ≤1 2 − 2 ) =3 1 θ 0 (1 − 0 7 2 ) 3π 11 = 6π ( − ) = 24 2 :)...
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This document was uploaded on 02/10/2014.

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