?edx e x?? 0 sin (???0 sindx e x?? 20 sin ?dx e x???2 sindx e x ,而???2 sindx e x?? 20 cos ?dx e x ) 2. 证明:??? 20 21 sin ?dxx x?? 20 21 cos ?dxx x (左-右= dx x x??? 20 21 )4 sin( 2 ??,然后用利用对称性计算积分的有关公式) 3. 证明:??? 1021 sin dxx x?? 1021 cos dxx x (通过换元将左、右积分分别比为? 20) sin(cos ?dtt 和? 20) cos(sin ?dtt ,然后比较被积函数的大小: ) sin 2 sin( ) cos(sin tt???,由tt cos sin 2 ???,得) sin 2 sin( ) cos(sin tt???。) 4.设)( ),(xgxf 在],[ba 上连续,且 1)(0??xg ,且)(xf 在],[ba 上单调减少,证明: ????????? aa ba bbdxxfdxxgxfdxxf)()()()( ,其中??? badxxg)( (可用变易常数法证。或: ?????? ba bbdxxfdxxgxf)()()(???????? ba bbdx xgxfdxxgxf]1)( )[()()(??????????? ba bbdx xgbfdxxgxf]1)([)()()(])()( )[()()(???????????? ba ba bbdxxgdxxgbfdxxgxf0)( )]()([????????badxxgbfxf 5.设l 表示椭圆 1 2 22 2??b ya x 的周长,证明: )(2)( 22balba??????(由弧长公式可得 dttbtal??? 20 2222 cos sin 4 ?,
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