一，概念及定義

概念

• 定積分是一個常量，而不定積分是函數(shù)（所有原函數(shù)）

  
  
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定積分的幾何意義

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二，定積分的性質(zhì)

<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，微積分基本公式

• 積分上限函數(shù)

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

• 積分上限函數(shù)的導數(shù)

<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，定積分的計算

微積分基本公式

• 計算定積分就是計算不定積分，區(qū)別在于不定積分加常數(shù) C,定積分加積分區(qū)間 ［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" />

第一換元法

<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" />

第二換元法

<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" />

分部積分法

<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" />

利用函數(shù)的奇偶性計算訂積分

<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" />

無窮區(qū)間的廣義積分

<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" />