3:(f+g,)(f(x)+(x)M(x)ac b f(xhh(x)dx+g(x)h(x)dx (∫,h)+(g,h) b 4.(f,f)=f2( r)ar ∫(x)≥0, (∫,∫)≥0. 且若∫(x)≠0,则∫2(x)>0,从而(f,∫)>0 故(,f)=0分∫(x) 因此,(f,g)为内积,C(a,b)为欧氏空间9 3 . ( , ) ( ) ( ) ( ) ( ) b a f g h f x g x h x dx + = +  ( ) ( ) ( ) ( ) b b a a = + f x h x dx g x h x dx   = + ( , ) ( , ) f h g h 2 4 . ( , ) ( ) b a f f f x dx =  2 f x( ) 0,    ( , ) 0. f f 且若 f x( ) 0,  则 2 f x( ) 0,  从而 ( , ) 0. f f  故 ( , ) 0 ( ) 0. f f f x =  = 因此， ( , ) f g 为内积， C a b ( , ) 为欧氏空间