# 微積分の計算について　　　N0.4　定積分の内容－1

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

##### 積分の手法　

$$ \int_a^b f(x)dx =\left[ F(x) \right]_{a}^{b} = F(b)-F(a)$$ 　　　　F(x)はf(x)の積分　

$$ \int_a^b f(x)dx =-\int_b^a f(x)dx  $$ ,$$   \int_a^a f(x)dx =0  $$ 

$$ \int_a^c f(x)dx = \int_a^b f(x)dx + \int_b^c f(x)dx $$

f(x)が偶関数なら　$$   \int_{-a}^{a} f(x)dx = 2 \int_0^{a} f(x)dx$$ 
奇関数なら$$   \int_{-a}^{a} f(x)dx = 0 $$ 


```python
from sympy import *
x, n , y, a = symbols('x n y a')
init_printing()
m ='3//5'
i =0
```

 ### 例題ー1


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


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


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


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


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


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


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


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


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


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


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


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


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


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


```python
expr =sqrt(1+(4/9)*x**(-2/3))
itg = Integral(expr,(x,0,1))
i=i+1
print( 'No.',m,'---',i)
itg
```


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


```python

```

7d90128b06155054603f35113782536a6ac7e2a3
ipynb
Jupyter Notebook
06_20181108-sekibun-6-1-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
06_20181108-sekibun-6-1-Ex&ans.ipynb
kt-pro-git-1/Calculus_Differential_Equation-public
d5deaf117e6841c4f6ceb53bc80b020220fd4814
MIT
06_20181108-sekibun-6-1-Ex&ans.ipynb
kt-pro-git-1/Calculus_Differential_Equation-public
d5deaf117e6841c4f6ceb53bc80b020220fd4814
MIT
Qwen/Qwen-72B
1. YES
2. YES