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Unformatted text preview: then I γ F · d r = 0 for any closed loop γ . (8) Consider the region R given by ≤ z ≤ ( yx 2 ) 2 , x 2 ≤ y ≤ x. Use the change of variables x = u, y = v + u 2 , z = wv 2 , to evaluate Z R dV yx 2 (9) Let R be the region where 0 ≤ y ≤ x and x 2 + y 2 ≥ 1. Evaluate Z R dA ( x 2 + y 2 ) 2 by switching to polar coordinates. (10) Which of the following is conservative: F = x i + e y j + xe y k or F = ye x i + e x j + z k Write it as ∇ f . (11) Evaluate Z C cos( πx ) dx + xdy where C is the following loop traversed clockwise6 2 1 2 1 (12) Determine Z dS √ x 2 + z 2 over the oblique cone parameterized by x = v + v cos( u ) , y = v sin( u ) , z = v for u ∈ [0 , 2 π ] and v ∈ [0 , 1]. (13) Compute the following integral by reversing the order Z 1 Z y y 2 1 1√ x dxdy...
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This note was uploaded on 06/03/2011 for the course PHYSICS 1B 1b taught by Professor Corbin during the Winter '10 term at UCLA.
 Winter '10
 Corbin

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