# 微積分の計算について　　　N0.4　定積分の内容－2　＜定積分の置換積分＞

###  学籍番号[＿＿＿＿＿＿＿＿＿]クラス[＿＿＿＿＿]　クラス番号[＿＿＿＿＿] 名前[＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿]

##### 置換積分の手法　

置換積分　公式ー１　　$   \int_{a}^{b} f(x)dx $　において 、$x = g(t)$ とおく
　$$   \int_{a}^{b} f(x)dx =  \int_{\alpha}^{\beta} f((g(t))g'(t)dt $$           ただし、$ a = g(\alpha) , b= g(\beta) $

もしくは　置換積分　公式ー２　$ t = g(x)$ とおく
　$$  \int_{a}^{b} f((g(x))g'(x)dx =  \int_{\alpha}^{\beta} f(t)dt $$           ただし、$ \alpha = g(a) , \beta= g(b) $


```python
from sympy import *
x, n , y, a = symbols('x n y a')
init_printing()
m ='4//2'
i =0
```


```python
expr = (x+1)**2
itg = Integral(expr,(x,2,3))
i=i+1
print( 'No.',m,'---',i)
itg
```


```python
simplify(itg.doit())
```


```python
expr = x*sqrt(2**2-x*x)
itg = Integral(expr,(x,0,2))
i=i+1
print( 'No.',m,'---',i)
itg
```


```python
simplify(itg.doit())
```


```python
expr = sqrt(3**2-x*x)
itg = Integral(expr,(x,0,3))
i=i+1
print( 'No.',m,'---',i)
itg
```


```python
simplify(itg.doit())
```


```python
expr = x / (x**2 +1)
itg = Integral(expr,(x,0,2))
i=i+1
print( 'No.',m,'---',i)
itg
```


```python
simplify(itg.doit())
```


```python
expr = 1/(1- x)**2
itg = Integral(expr,(x,2,4))
i=i+1
print( 'No.',m,'---',i)
itg
```


```python
simplify(itg.doit())
```


```python
expr = x/sqrt(4+x**2)
itg = Integral(expr,(x,0,1))
i=i+1
print( 'No.',m,'---',i)
itg
```


```python
simplify(itg.doit())
```


```python
expr = (sin(x)**2 )*cos(x)
itg = Integral(expr,(x,0,pi/2))
i=i+1
print( 'No.',m,'---',i)
itg
```


```python
simplify(itg.doit())
```


```python
expr = 1/(x*log(x))
itg = Integral(expr,(x,exp(1),exp(1)**2))
i=i+1
print( 'No.',m,'---',i)
itg
```


```python
simplify(itg.doit())
```


```python

```

6427932c0bab6ea497ca8e97954f6b8430a17ad0
ipynb
Jupyter Notebook
07_20181118-sekibun-6-2-Ex&ans.ipynb
kt-pro-git-1/Calculus_Differential_Equation-public
d5deaf117e6841c4f6ceb53bc80b020220fd4814
MIT
2019-07-10T11:33:18.000Z
2019-07-10T11:33:18.000Z
07_20181118-sekibun-6-2-Ex&ans.ipynb
kt-pro-git-1/Calculus_Differential_Equation-public
d5deaf117e6841c4f6ceb53bc80b020220fd4814
MIT
07_20181118-sekibun-6-2-Ex&ans.ipynb
kt-pro-git-1/Calculus_Differential_Equation-public
d5deaf117e6841c4f6ceb53bc80b020220fd4814
MIT
Qwen/Qwen-72B
1. YES
2. YES