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url: /notes/高等数学/一元函数积分学/index.md
---
## 不定积分的概念与性质

![image-20220221174214693](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211742772.png)

![image-20220221174229681](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211742842.png)

![image-20220221174248045](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211742185.png)

## 换元积分法(和差化积/积化和差)

![image-20220221174315298](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211743437.png)

![image-20220221174407714](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211744792.png)

![image-20220221174430407](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211744449.png)

![image-20220221174443929](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211744045.png)

![image-20220221174500459](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211745583.png)

## 分部积分法

![image-20220221174519387](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211745443.png)

## 有理函数的积分

![image-20220221174538835](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211745004.png)

![image-20220221174552466](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211745582.png)

![image-20220221174615111](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211746327.png)

## 积分表的使用

![image-20220221174637860](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211746904.png)

![image-20220221174656011](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211746076.png)

![image-20220221174741090](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211747154.png)

![image-20220221174804354](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211748433.png)

![image-20220221174821930](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211748996.png)

![image-20220221174841527](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211748591.png)

![image-20220221174901429](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211749508.png)

![image-20220221174921342](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211749422.png)

![image-20220221174936754](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211749829.png)

![image-20220221174952327](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211749400.png)

![image-20220221175012892](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211750988.png)

![image-20220221175035570](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211750654.png)

![image-20220221175054135](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211750219.png)

![image-20220221175109065](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211751148.png)

![image-20220221175122438](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211751505.png)

## 定积分的概念与**性质**

![image-20220221175153497](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211751621.png)

![image-20220221175214194](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211752284.png)

![image-20220221175230001](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211752083.png)

## 函数的积分上限及其导数

![image-20220221175254985](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211752206.png)

## 牛顿\*\*-\*\*莱布尼茨公式

![image-20220221175314448](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211753543.png)

## 定积分的换元法

![image-20220221175331494](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211753550.png)

## 定积分的分部积分法

![image-20220221175347855](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211753927.png)

## 积分在几何学上的应用

![image-20220221175410626](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211754764.png)

![image-20220221175425802](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211754930.png)

![image-20220221175436257](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211754368.png)

![image-20220221175446947](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211754026.png)

![image-20220221175500488](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211755559.png)

![image-20220221175518278](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211755528.png)

![image-20220221175534406](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211755481.png)

![image-20220221175549471](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211755549.png)

![image-20220221175602712](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211756815.png)

![image-20220221175617383](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211756439.png)