x+C f(x)(x-xo lx=If(r) 8(x-xo dx f(5) x0-8<5<x+E 注意:δ也能表示连续分体的函数 f(t=f(o)8(t-tdt=f([)8(t-t di
e x e x d d e e - < < + = - = - ò ò + - ¥ -¥ x x f f x x x dx f x x x dx x x 0 0 0 ( ) ( ) ( ) ( ) ( ) 0 Q 注意: d也能表示连续分体的函数 f t f t d t t dt f t d t t dt b ò òa = - = - ¥ -¥ ( ) ( ) ( ) ( ) ( )
2、若定义6(x)=8'(x)-6涵数的导数 d x 则(1)|f(x)6(x-x0)x=f(x) (2)x-x)6(x-x0)=-6(x-x0) (3)(x)6x-x)x=(-1)(x)
2、若定义 d (x) = d '(x) - d函数的导数 dx d (3) ( ) ( ) ( 1) ( ) (2)( ) '( ) ( ) (1) ( ) '( ) '( ) 0 ( ) 0 0 0 0 0 0 f x x x dx f x x x x x x x f x x x dx f x n n n - = - - - = - - - = - ò ò ¥ -¥ ¥ - ¥ d d d 则 d
证()x(x-xk =|(xd6(x-x) f(x6(x-x6)120-/(x)6(x-x6)x f"(x0)
f x x x dx ò ¥ -¥ :(1) ( ) '( - ) 0 证 d '( ) ( ) ( ) | '( ) ( ) ( ) ( ) 0 0 0 0 f x f x x x f x x x dx f x d x x = - = - - - = - ò ò ¥ -¥ ¥ -¥ ¥ -¥ d d d