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Unformatted text preview: and j r ( t ) j = 2 and we have Z C ( x + y ) ds = Z &= 2 (2 cos ( t ) + 2 sin ( t )) (2) dt = 8 . 3) Let V ( x; y ) be the velocity ±eld V ( x; y ) = x i + y j . 1 Find the &ow along and the &ux across the curve r ( t ) = cos ( t ) i + sin ( t ) j & t & & . Solution: Here we have M ( x; y ) = x , N ( x; y ) = y , dx=dt = ± sin ( t ) and dy=dt = cos ( t ) . The &ow is thus Z & ((cos ( t )) ( ± sin ( t )) + (sin ( t )) (cos ( t ))) dt = 0 and the &ux is Z & ((cos ( t )) (cos ( t )) ± (sin ( t )) ( ± sin ( t ))) dt = & . 2...
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 Fall '10
 Ellermeyer
 Math, Sin, Cos, Trigraph, dx dy

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