6.3 定积分的基本性质

0?? ii nixfk?????)( lim 1 0??( )d . ba k f x x ??性质 2补充:不论的相对位置如何, 上式总成立.cba,, 例若,cba??( )d ca f x x ?( )d ( )d b c a b f x x f x x ? ?? ?( )d ba f x x ?( )d ( )d c c a b f x x f x x ? ?? ?( )d ( )d . c b a c f x x f x x ? ?? ?(定积分对于积分区间具有可加性) 则假设bca??性质 3性质 4性质 5 ??[ ( ) ( )] ba g x f x dx ??推论 1推论 2解令,)(xexf x??]0,2[??x,0)(?xf? 02 ( )d 0, x e x x ?? ??? 02d x e x ??? 02 d , x x ???于是 20d x e x ?? 20 d . x x ???证,)(Mxfm??? d ( )d d , b b b a a a m x f x x M x ? ??? ? ?( ) ( )d ( ). ba m b a f x x M b a ? ? ???(此性质可用于估计积分值的大致范围) 性质 6xO yM ab m