ex5设f(x)在(-∞,+0)可积,证明 ∫(z)hv=n[1(1-x2)(x)x9:x2+y2+z2sL Pr0of.-1≤z≤1, D.:x2+12≤1 Q D 丌(1-x)f(x)dz =[,(1-x2)f(x)x K心( ) (1 ) ( ) , : 1. 5. ( ) ( , ) , 1 2 2 2 1 2 = −  + +  −  +   −  f z dv x f x dx x y z ex f x  设 在 可 积 证 明 Proof. − 1  z  1, : 1 . 2 2 2 D x y z z +  −    −   = Dz f z dv f z dz dxdy 1 1 ( ) ( ) − = − 1 1 2  (1 z ) f (z)dz (1 ) ( ) . 1 1 2 − =  − x f x dx