[高等教育]第五章第2節(jié)微積分基本公式-文庫吧資料
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【正文】 xa??? ? ? )( bxa ?? . 積分上限函數(shù)的性質(zhì) xx ??證 dttfxx xxa??????? )()()()( xxx ????????dttfdttf xaxxa ?? ?? ?? )()()(x?x5 ?dttfdttfdttf xaxxxxa ??? ??? ? )()()( ?,)(? ?? xxx dttf?由積分中值定理得 xf ???? )(? ],[ xxx ????,0 xx ?? ??),(???? fx ? ).(limlim00 ?????? fx xx ?? ?).()( xfx ???a b xyo xx ??)(x?x6 、變限積分求導(dǎo)公式2)())(()1( xfdttfxa ???)())(())(()2( )( xuxufdttfxua ????)())(())(()3( )( xvxvfdttfb xv ?????)())(()())(())(()4( )( )( xvxvfxuxufdttfxu xv ??????）（ 2證明 ))(())(( )()( dttfdxddttf xuaxua ?? ??dxxdudttfxdud xua)())(()()( ?? ?).())(( xuxuf ??7 25( ) s i n , ( )xF x t d t F x?? ? 求例 1解 2( ) s i n ( ) ( )F x x x??? 1s i n2x x??例2 sin 4( ) 2 , ( ) .xxF x t d t F x???? 求4( ) 2 s i n ( s i n )F x x x??? ? ?42 x??解 ? s in .2 xx44c o s 2 s i n 2 .x x x? ? ? ?8 例 3 求 2c o s120l i m .x txe d tx???解 2c o s1x td e d tdx ??因2c o s ( c o s )xex? ??? 2c o ss i n ,xxe ?? ? ?2c o s120limx txe d tx??? 2c o s0s i nlim 2 xxxex ?????1 1 .22e e?? ? ? ?所以由洛必塔法則 9 例 4 設(shè) )( xf 在 ),( ???? 內(nèi)連續(xù) , 且 0)( ?xf . 證明函數(shù)???xxdttfdtttfxF00)()()(在 ),0( ?? 內(nèi)為單調(diào)增加函數(shù) . 證 ?x dtttfdxd 0 )( ),( xxf? 0 ()xd f t d tdx ? ),( xf?? ?2000)()()()()()(??? ???xxxdttfdtt
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