北大版高等数学课后答案7.pdf

课后答案网 5p Æ6 1Ù SK )‰ SSSKKK 7.1 3. ¼ f (x, y)3 k. 4 Dþë Y, g (x, y)3 Dþš K, g (x, y)†f (x, y)g (x, y)3 Dþ ŒÈ . y ²: 3 D ¥3 ˜ :(x , y ) f (x, y)g (x, y)dσ = f (x , y ) g (x, y)dσ. 0 0 0 0 D D y . m, M Ǒf 3 Dþ  ,  ŒŠ . Kmg (x, y) ≤ f (x, y)g (x, y) ≤ Mg (x, y). Ïd mg (x, y)dσ ≤ f (x, y)g (x, y)dσ ≤ Mg (x, y)dσ. D D D g (x, y)dσ = 0, f (x, y)g (x, y)dσ = 0, e K Œ?  ˜ :(x , y ) ∈ D · K 0 0 D D f (x,y)g (x,y)dσ D . Ä Kkm ≤ ≤ M . d0Š ½n , 3 (x , y ) ∈ D  ¤ á 0 0 g (x,y)dσ D f (x,y)g (x,y)dσ D , f (x, y)g (x, y)dσ = f (x , y ) g (x, y)dσ. f (x , y ) = = 0 0 0 0 g (x,y)dσ D D D 4. ¼ f (x, y)3 k . 4 Dþ ë Y, š K, f (x, y)dxdy = 0. y D ² f (x, y) = 0, (x, y) ∈ D . y . ÏǑf š K, ef Ø ? ? Ǒ , Kf 3 , :P ∈ D? Œ u0. q Ïf ë Y, Ïd 1 3 P ˜‡  Sf Š Œu 2 f (P ). u f (x, y)dxdy 0, gñ . D SSSKKK 7.2 OŽ e­È© . 3. ydxdy , ¥D dy = 09y = sin x (0 ≤ x ≤ π)¤ . D π sin x π 2 I = dx dyy = dx sin x = π . 0 0 0 2 4 2 ¥D dx = 1, y2 = 4x¤ . 4. xy dxdy ,