(7.3)James Stewart Calculus 5th
2016-10-30 本文已影响23人
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Trigonometric Substitution 三角替换
对应的三角替换的表格
![](https://img.haomeiwen.com/i2800913/a1319f29d50bcc1f.png)
例子
一些例子
例子1
![](https://img.haomeiwen.com/i2800913/011debefa3e2a12e.png)
设
![](https://img.haomeiwen.com/i2800913/c25b6806681b223f.png)
范围
![](https://img.haomeiwen.com/i2800913/612e6b0693d4154f.png)
有
![](https://img.haomeiwen.com/i2800913/77b6a5345def3a5d.png)
可以化简为:
![](https://img.haomeiwen.com/i2800913/e0ea920f95540c0f.png)
这个时候
![](https://img.haomeiwen.com/i2800913/02b8cf731eeacfaa.png)
所以
![](https://img.haomeiwen.com/i2800913/fea102cb9110cabb.png)
例子2
![](https://img.haomeiwen.com/i2800913/e8930890517bd50c.png)
先化简
![](https://img.haomeiwen.com/i2800913/0b2e8b566ee7f554.png)
可以得到:
![](https://img.haomeiwen.com/i2800913/f11d923f9a48d878.png)
得:
![](https://img.haomeiwen.com/i2800913/c6c431ac74d975cd.png)
参考图像:
![](https://img.haomeiwen.com/i2800913/c2c011c3cde94dea.png)
可以知道,先求 A/4 ,就可以求出A
![](https://img.haomeiwen.com/i2800913/956f41a3cfc7fd5e.png)
有:
![](https://img.haomeiwen.com/i2800913/42ff61345a860818.png)
范围从[0,a] 变成[0,π/2]
所以
![](https://img.haomeiwen.com/i2800913/622e3f689746bb9c.png)
对应的三角替换的表格
一些例子
例子1
例子2