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s? dxxf( 2) ? ?0 )( s i n dxxxf ? ??? ? ??0 )][ s i n ()( dxxfx?? ?? ?? ? 00 )( s i n)( s i n dxxxfdxxf.)( s in2)( s in 00 ?? ?? ??? dxxfdxxxf? ? ?0 2c os1 s i n dxxxx ? ? ??? 0 2c os1 s in2 dxxx? ? ???? 0 2 )( c osc os1 12 xdx? ????? 0)ar c t a n ( c os2 x)44(2 ??????? .42??例 9 設(shè) )( xf 在 ],[ ??? 上連續(xù),且 )(,s i n)(c o s1)(2xfxdxxfxxxf 求???????. 解 ,s i n)( Ax d xxf ?????設(shè) Axxxf ??? 2c o s1)(則,)s i nc o s1 s i n(s i n)( 2?? ?? ????? ? ?? ? dxxAxxxxdxxfA? ?? ?0 2c o s1 s i n2 dxxxx ? ??? ?? 0 2c o s1 s i n22 dxxx? ??? 0)a r c t a n( c o s x?? .22??.2co s1)(22????? xxxf例 10 計(jì)算 解 ? ???a adxxax0 22 )0(.1令 ,s in tax ?ax? ,2??? t 0?x ,0?? t,c o s td tadx ?原式 ????? 20 22 )s i n1(s i nc os dttatata????20 c o ss inc o s dtttt? ? ?????????? 20 c oss i ns i nc os121 dttttt? ? 20c o ss inln21221 ?????? ??法二 : 原式 ? ?? 20 c o ss i n c o s?dttt t.4??? ?? 20 s i nc o s s i n?dtttt? ???? 20 )c o ss i n s i nc o ss i n c o s(21?dttt ttt t? ?? 20 121?dt?????? 20)2c o s ()2s i n ()2c o s (????dtttt例 11 原式 ? ?362)2(c o s?? ? dxxxx求.2ln1???????? 362)]2(2)[2()2(c o s?? ????dxxxx362ln21???? xx??解 ? ?? 362)2(s i n?? ? dxxxx ???? 3622)2(c o ss i n21 ?? ? dxxxxx? ??? 36)221(2 1?