prac exam 2A solutions

We can use eg m x y 3 3 x3 1 f n ds 7 a

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Unformatted text preview: M such that −My = (x + y )2 . We can use e.g. M = − (x + y )3 . 3 x3 1 ˆ F · n ds = 7. a) div F = 2y , so C R 1 2y dydx = 2y dA = 0 0 −(1 + y 2 ) 0 1 x6 dx = . 7 ˆ ˆ b) For the flux through C1 , n = −ˆ implies F · n = = −1 where y = 0. The length of C1 ˆ is 1, so the total flux through C1 is C1 (−1) ds = −1. The flux through C2 is zero because n = ˆ ı and F ⊥ ˆ. ı 8 1 ˆ ˆ ˆ ˆ c) F · n ds = F · n ds − F · n ds − F · n ds = − (−1) − 0 = . 7 7 C3 C1 +C2 +C 3...
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