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66高中数学选修系列选修《微积分基本定理与定积分计算》教案.pdf

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1、41/24 3 微积分基本定理与定积分计算一、目标预览1.理解并能熟练运用微积分基本定理.2.掌握定积分的常用计算方法.3.了解定积分与不等式的常用证明方法.4.了解定积分相关知识的综合应用.二、概念入门设,baRf，称函数xadttfx)()(),(bax为函数)(xf在,ba上的变上限定积分；类似地可定义变下限定积分：bxdttfx)()(.注i）由)(R积分的性质，)(x的定义有意义.ii）由)(R积分的性质易证,)(baCx.三、主要事实1.微积分基本定理若,baCf，则)()(xfx),(bax，即xaxfdttfdxd)()(，,bax.注i）证明由导数的定义及第一积分中值定理即得

2、.ii）通过微分中值定理微积分基本定理及其等价表述沟通了不定积分与定积分、微分与积分的内在联系.iv）利用微积分基本定理及复合函数微分法可得下述的变限42/24)()()()()()()(xxxxfxxfdttfdxd)()()()(abadxxfagdxxgxfbdxxgbf)()(积分求导公式：若,baCf，)(x、)(x在,dc上可微而且),(dc、,),(badc，则2.第二积分中值定理1）旁内 Bonnet，1819-1892 法）型第二积分中值定理）若,baRf，而且)(xg是,ba上非负递减相应地递增）函数，则存在,ba使得相应地）2）Werierstrass型第二积分中

3、值定理）若,baRf，)(xg是,ba上的单调函数，则存在,ba使得babadxxfbgdxxfagdxxgxf)()()()()()(.证1）令xadttfxF)()(),(bax，利用g的可积性得iixxiniTbadxxfxgdxxgxf110|1)()(lim)()()()()(lim1110|iiiniTxFxFxg再由)()()(111iiinixFxFxg)()()()()(1111niiinixgbFxgxgxF文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档

4、编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E

5、6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3

6、 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6

7、文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y

8、9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2

9、W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8

10、K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K643/24 及g的单调减小性，可得)()()()(maxminagFdxxgxfagFba再由连续函数的介值性即得.2）当g为单调递减增）时，对)()()(bgxgxh)(xg)(ag应用 1）即得.3.定积分的计算1）牛顿莱布尼兹公式）若,baRf，,baCF而且除有限个点外有)()(xfxF，那么有baaFbFdxxf)()()(.注i）牛顿莱布屁兹公式简称LN公式，它是微积分的核心定理，最初分别由牛顿与莱布尼兹在17 世纪

11、下半叶独立得到，柯西在19 世纪初给出精确叙述与证明，黎曼在19 世纪中叶给予完善，达布在1875 年给出现在这种形式.ii）证明可由)(R积分的定义分点包括例外点）及微分中值定理作用在F上）可推得.2）定积分换元积分法）如果)(t在,上有连续导数，a)(，b)(，,),(ba，,baCf，那么有badtttfdxxf)()()(注i）定积分换元积分公式由复合函数微分法及LN公式可得，而且,)(baCt可减弱为,R.进一步，定积分换元积分公式中的,baCf可减弱为,baRf，但的条件稍许加强证明较为复杂），即有以下的命题成立：若,baRf，,:ba是一一映射而且还满足文档编码:CQ3A8A

12、7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1

13、C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10

14、H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A

15、8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6

16、U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J

17、10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ

18、3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K644/24 a)(，b)(，,)(Rt，那么有badtttfdxxf)()()(.ii）定积分换元积分法实际上是不定积分第二换元积分法的直接应用.但使用时有较大差别，在这里换元之后变量不需回代，但积分限要跟着更换在去掉根号的情形下须注意函数的符号）.iii）对应于不定积分中的第一换元法

19、即凑微分法），在这里可以不加变动地直接应用，而且积分限也不须作更改即仍然采用原来的积分变量）.3）分部积分法）如果u、v具有连续的导数，那么有babaxdvxudxxvxu)()()()(babaxduxvxvxu)()(|)()(.注i）分部积分可由乘积微分法则及LN公式直接证之.ii）分部积分公式可连续使用n次，即利用数学归纳法及分部积分公式可得下面的命题：若u、v具有1n阶连续导数，那么有bandxxvxu)1()()(bannnnxvxuxvxuxvxu|)()()1()()()()()()1()(banndxxvxu)1(1)()()1(),3,2,1(n.4.定积分计算中常用的几个

20、公式1）若,baCf，则babadxxbafdxxf)()(badxxbafxf)()(21.文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ

21、3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9

22、C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F

23、4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:

24、CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 H

25、Y9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP

26、5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K645/24 2）若,aaCf，则aaadxxfxfdxxf0)()()(为奇函数为偶函数f，fdxxfa0,)(203）若)(xf是以T为周期的周期函数，则1Ra有T/2

27、2/0)()()(TTTaadxxfdxxfdxxf4）若 1,0Cf，则2020)(cos)(sindxxfdxxf.5）若 1,1Cf，则2000)(sin)(sin2)(sindxxfdxxxfdxxxf.证1）令tbax可得.2）令tx得aadttfdxxf00)()(.3）令Ttx得aaTaTdttfdtTtfdxxf00)()()(，于是有TTaTTaTaadxxfdxxfdxxfdxxf0)()()()(，再令2Ta得T/dxxfdxxf02/2-)()(.4）令tx2/可得.5）令tx可得000)(sin)(sin)(sindtttfdttfdxxxf文档编码:CQ3A8A7Y

28、9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2

29、W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8

30、K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A

31、7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1

32、C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10

33、H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A

34、8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K646/24 及202)(sin)(sindttfdxxf.5.带积分余项的泰勒公式若)(xf在,ba上具有1n阶连续导数，那么,0baxx有xxnnkknkdttxtfnxxkxfxf)1(00)(00)(!1)(!)()(，即xxnnndttxtfnxR)1(0)(!1)(

35、，称此为泰勒公式的积分余项.注i）令nknktxktfxftF)(!)()()()(0常数变易法），对)(tF分别应用LN公式及分部积分公式即获得积分余项公式的证明.ii）对积分余项应用第一积分中值定理ntxtg)()(在积分区间,0 xx或,0 xx上不变号）可得泰勒公式的拉格朗日余项：10)1()()!1(1)(nnnxxfnxR其中10),(00 xxx）.iii）对积分余项应用积分平均值定理泰勒公式的柯西余项：)()(!1)(0)1(xxxfnxRnnn)10()()1)(!11000)1(nnnxxxxxfn四、例题选讲1.定积分计算例题选.文档编码:CQ3A8A7Y9E6 HY9C

36、6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4

37、J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:C

38、Q3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY

39、9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5

40、F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码

41、:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6

42、HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K647/24 例 1 求下列定积分1）2024dxxx2）202cossintdtt3）1021dxx4）1021)1ln(dxxx5）exdxx02ln6）ln2021dxex7）42)3ln()9ln()9ln(dxxxx8）44-21sindxexx9）221111dxexxxx解1）20202322

43、238|)4(31)4(421xxdx.2）20203231|cos31coscostttd.3）令txsin，3）4|)2sin21(21cos20202tttdt4）令txtan，4）40tant)ln(1dt4040cos)4/(sin(2lncossincoslndxxxdxxxx.令tx4得4040cosln)4sin(lntdtdxx，于是有4）2ln8|2ln2140 x.5）eeedxxxxxxd112133)|ln(31)(ln31)12(913e文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1

44、C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10

45、H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A

46、8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6

47、U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J

48、10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ

49、3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9

50、C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K6文档编码:CQ3A8A7Y9E6 HY9C6U1C2W3 ZP5F4J10H8K648/24 6）2ln022ln02|1)(1xxxxeeede2ln02)32ln(231dxeexx7）利用babadxxabfxfdxxf)()(21)(得7）42121dx8）利用aaadxxfxfdxxf-0)()()(得8）402418sinxdx9）221252212211123|exdedxexxxx.例 21）求202sinxdxIn2）证明 Wallis公式：2!)!12

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关键词：: 微积分基本定理与定积分计算 66 高中数学选修系列微积分基本定理积分计算教案

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本文标题：66高中数学选修系列选修《微积分基本定理与定积分计算》教案.pdf
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