定积分

一，概念及定义

概念

• 定积分是一个常量，而不定积分是函数（所有原函数）

  
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定积分的几何意义

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二，定积分的性质

<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-6.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-7.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-8.png" width="500" />

二，微积分基本公式

• 积分上限函数

<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-9.png" width="500" />

• 积分上限函数的导数

<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-10.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-11.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-12.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-13.png" width="500" />

三，定积分的计算

微积分基本公式

• 计算定积分就是计算不定积分，区别在于不定积分加常数 C,定积分加积分区间 ［a,b］ ）

<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-14.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-15.png" width="500" />

第一换元法

<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-16.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-17.png" width="500" />

第二换元法

<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-18.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-19.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-20.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-21.png" width="500" />

分部积分法

<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-22.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-23.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-24.png" width="500" />

利用函数的奇偶性计算订积分

<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-25.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-26.png" width="500" />

无穷区间的广义积分

<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-27.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-28.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-ding-jifen-29.png" width="500" />