5-3證明定積分公式-文庫吧
2025-04-24 21:07 本頁面
【正文】 ?20 24 1tx tan2? ?4?0 tdt t a n2t a n4412??? 40 s e c1?x tdt2sec40]t a ns e c[ln?tt ??)12l n( ??6例 ],[)( aaCxf ??證明：若為奇函數(shù)時 )( .1 0 xf ??aa dxxf )(a? axy00?為偶函數(shù)時 )( .2 0 xf ??aa dxxf )(a? a xy0?? a dxxf0 )(2? ??? ? ??a a aa dxxfdxxfdxxf 00 )()()(證 ??0 )(a dxxf ? ??0 )()(a tdtf ? ?? a dttf0 )(tx ??? ?? a dttf0 )( ?? a dxxf0 )(? ??? a dxxfxf0 )]()([為奇函數(shù)時 )( .1 0 xf ??aa dxxf )(為偶函數(shù)時 )( .2 0 xf ??aa dxxf )( ?? a dxxf0 )(20??? ??1 1 22 )c os1( dxx xx7例?? ?? 1 1 22 dxxx?? ?? 1 1 22c o s dxxxx奇函數(shù)偶函數(shù)? ?? 10 222 dxxx? ?? 10 222 1 dxx? ?? ??10 212 )2( x )2( 2xd ?10212 ])2[(2 x??? )21(2 ???tx ?? 2 ?令8例 試證：設(shè) ],1,0[)( Cxf ?? 20 )( s i n .1?dxxf ?? 20 )( c o s?dxxf證 xx c oss i n ?為使0? 20 )( s i n?dxxftx ?? 2? ?)]2[ s i n( tf ?? )2(d ??2?dt? 0?2?)(cos tf? ?? 20 )( c o s?dxxf? ?? ? ?0 )( s i n)( dttft? ?0 )( s i n .2 dxxxf ?? ?? 0 )( s i n2 dxxf證tx ?? ? ?0? )( t?? )][ s i n( tf ?? )( td ??? ??? 0 )( s i n dttf ? ?? 0 )(sin dtttf? ??? 0 )( s i n dxxf?? ?? ?? ? 00 )( s i n2)( s i n dxxfdxxxf??0 )(sin dxxxf?? ?0 )( s i n dxx
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