大一定积分
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/13 23:41:38
大一定积分
![](http://img.wesiedu.com/upload/0/da/0da677f9ab67dfe0c14ee684a259e9ca.jpg)
![](http://img.wesiedu.com/upload/0/da/0da677f9ab67dfe0c14ee684a259e9ca.jpg)
![大一定积分](/uploads/image/z/18917671-31-1.jpg?t=%E5%A4%A7%E4%B8%80%E5%AE%9A%E7%A7%AF%E5%88%86%26nbsp%3B)
d/dx ∫(0→e^(- x)) ƒ(t) dt = e^x
[- e^(- x)]ƒ[e^(- x)] = e^x
ƒ[e^(- x)] = e^x/[- e^(- x)] = - e^(2x)
令y = e^(- x)
- x = lny
x = - lny
ƒ(y) = - e^[2(- lny)] = - 1/e^(2lny) = - 1/e^(lny²) = - 1/y² = - y^(- 2)
∴ƒ(x) = - x^(- 2)
[- e^(- x)]ƒ[e^(- x)] = e^x
ƒ[e^(- x)] = e^x/[- e^(- x)] = - e^(2x)
令y = e^(- x)
- x = lny
x = - lny
ƒ(y) = - e^[2(- lny)] = - 1/e^(2lny) = - 1/e^(lny²) = - 1/y² = - y^(- 2)
∴ƒ(x) = - x^(- 2)