prac exam 2B solutions

Hence f n 0 therefore the ux of f through c4 equals 0

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Unformatted text preview: ) • R 0 0 0 ydxdy R ydy = [y 2 /2]4 = 8. 0 ˆ ˆ b) On C4 , x = 0, so F = − sin y ˆ, whereas n = −ˆ. Hence F · n = 0. Therefore the flux of F ı through C4 equals 0. Thus C1 +C2 +C3 ˆ F · n ds = C ˆ F · n ds − C4 ˆ F · n ds = C ˆ F · n ds ; and the total flux through C1 + C2 + C3 is equal to the flux through C . 5. Let u = 2x − y and v = x + y − 1. The Jacobian ux uy v x vy 2 −1 11 = = 3. 1 Hence dudv = 3dxdy and dxdy = dudv , so that 3 V 1 (4 − u2 − v 2 ) dudv 3 (4 − (2x − y )2...
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