010.102-2007-2-fin

# 010.102-2007-2-fin - 2(12 15 1:00-3:00 200 1(30 D Z Z 2(a...

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2 (12 15 1:00-3:00) : : .( 200 ) 1. (30 ) D . (a) Z Z D e x 2 dxdy , D : x y 2 x , 0 x 2 . (b) Z Z D p 1 + y 5 dxdy , D : 4 x y 1, 0 x 1. (c) Z Z Z D ( x 2 + y 2 ) dxdydz , D : 2 x 2, 4 x 2 y 4 x 2 , p x 2 + y 2 z 2. 2. (a) (15 ) . Z −∞ e x 2 dx, Z −∞ x 2 e x 2 dx. (b) (10 ) (a) 결과 , g ( x ) = Ae Bx 2 . ( , A, B > 0 .) Z −∞ g ( x ) dx = 1 , Z −∞ x 2 g ( x ) dx = 1 . 3. (30 ) S . S = { ( x, y, z ) R 3 | x 2 + y 2 + z 2 = 4 , z 1 } . 4. (30 ) 위의 D = { ( x, y ) | x 2 + 2 y 2 1 } .
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