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x≤b, Q y1(x)≤y≤y2(x) 1(x,y)≤=≤=2(x,y), 相应的积分表达式为: y2(x) 2(x,y) f(x,y, =)dv= dx.dy (r,y)y(x,y, z)d (2)柱面坐标系下:常将柱形域表为 a≤z≤b a≤b≤B, r1(6)≤r≤F2(6) 相应的积分表达式为 ∫/(xy,=J( rose,rsin-)rd ra∫d∫m n(e)y(rcos 0, rsin 0, x)rdr (3)球面坐标系下:常将球形域表为 Q B1≤6≤B2 1(0,9)≤p≤P2(O,q 相应的积分表达式为: QU(x, J=)dv=[I/(psin p cose, psin prsin 0, pcos p)psin o dp de do do[ deo f(psin o cos e, psin (p sin 0, pcos o)p' sin pdp (6;) :            ( , ) ( , ), ( ) ( ), , 1 2 1 2 z x y z z x y y x y y x a x b 相应的积分表达式为:     =  b a z x y z x y y x y x f x y z V x y f x y z z ( , ) ( , ) ( ) ( ) 2 1 2 1 ( , , )d d d ( , , )d (2)柱面坐标系下:常将柱形域表为  :            ( ) ( ). , , 1  2     r r r a z b 相应的积分表达式为   =   f (x, y,z)dV f (r cos,rsin ,z)rdrddz =    ( ) ( ) 2 1 d d ( cos , sin , ) d        r r b a z f r r z r r . (3)球面坐标系下:常将球形域表为  :            ( , ) ( , ). , , 1 2 1 2 1 2              相应的积分表达式为:   =   ( , , )d ( sin  cos,  sin  sin ,  cos) sin  d d d 2 f x y z V f r              =              ( , ) ( , ) 2 2 1 2 1 2 1 d d f ( sin cos , sin sin , cos ) sin d . x D y z a O b 1 2 D x y a b   O z D x y z O 1 2 2 1
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