换元法、分部积分法.ppt

2023/8/18,1,第三节 换元法,2023/8/18,2,2023/8/18,3,一、换元公式,2023/8/18,4,温馨提示:,换元的同时要换限,2023/8/18,5,例2 计算,解:,注意:,对应关系,换元后，积分上下限相应改变,换元必换限,2023/8/18,6,例3 计算,解:,换元必换限,2023/8/18,7,例4 计算,解：令,2023/8/18,8,2023/8/18,9,2023/8/18,10,奇函数,例6 计算,解:,原式,偶函数,单位圆的面积,2023/8/18,11,2023/8/18,12,2023/8/18,13,2023/8/18,14,2023/8/18,15,2023/8/18,16,技巧:,定积分的换元法,小结,2023/8/18,17,二、分部积分法,乘积函数求定积分,2023/8/18,18,2023/8/18,19,例1 计算,解：合理选择u,v令,2023/8/18,20,例2 计算,2023/8/18,21,例3 计算,解,2023/8/18,22,2023/8/18,23,选一、换元公式,2023/8/18,24,2023/8/18,25,2023/8/18,26,2023/8/18,27,2023/8/18,28,2023/8/18,29,2023/8/18,30,2023/8/18,31,2023/8/18,32,2023/8/18,33,2023/8/18,34,