# Cálculo


```python
from sympy import *
```


```python
x = Symbol('x')
```

DERIVADAS


```python
x**2 + sin(x)
```




    x**2 + sin(x)




```python
# Para arrumar a função.
init_printing(pretty_print=True)
```


```python
x**2 + sin(x)
```




$$x^{2} + \sin{\left (x \right )}$$




```python
# Para calcular a Derivada.
(x**2 + sin(x)).diff(x)
```




$$2 x + \cos{\left (x \right )}$$




```python
# Para calcular a 2ª Derivada.
(x**2 + sin(x)).diff(x,2)
```




$$- \sin{\left (x \right )} + 2$$




```python
# Para ver a expressão arrumada.
Derivative(x**2 + sin(x))
```




$$\frac{d}{d x} \left(x^{2} + \sin{\left (x \right )}\right)$$




```python
# Para calcular a Derivada.
Derivative(x**2 + sin(x)).doit()
```




$$2 x + \cos{\left (x \right )}$$



INTEGRAL INDEFINIDA


```python
# Para calcular a Integral.
integrate(x**2 + sin(x))
```




$$\frac{x^{3}}{3} - \cos{\left (x \right )}$$




```python
# Integral antes de resolver.
Integral(x**2 + sin(x))
```




$$\int \left(x^{2} + \sin{\left (x \right )}\right)\, dx$$




```python
# Para resolver a integral.
Integral(x**2 + sin(x)).doit()
```




$$\frac{x^{3}}{3} - \cos{\left (x \right )}$$




```python
# Integral antes de resolver arrumada.
Integral(x**2 + 2 + sin(x) * exp(x))
```




$$\int \left(x^{2} + e^{x} \sin{\left (x \right )} + 2\right)\, dx$$




```python
# Para resolver a Integral.
Integral(x**2 + 2 + sin(x) * exp(x)).doit()
```




$$\frac{x^{3}}{3} + 2 x + \frac{e^{x} \sin{\left (x \right )}}{2} - \frac{e^{x} \cos{\left (x \right )}}{2}$$



INTEGRAL DEFINIDA


```python
# Integral definida antes de resolver arrumada.
Integral(x**2 + 2 + sin(x) * exp(x),(x, 0, 2))
```




$$\int_{0}^{2} \left(x^{2} + e^{x} \sin{\left (x \right )} + 2\right)\, dx$$




```python
# Para resolver a Interal definida.
Integral(x**2 + 2 + sin(x) * exp(x),(x, 0, 2)).doit()
```




$$- \frac{e^{2} \cos{\left (2 \right )}}{2} + \frac{e^{2} \sin{\left (2 \right )}}{2} + \frac{43}{6}$$




```python
# Resultado numéerico.
Integral(x**2 + 2 + sin(x) * exp(x),(x, 0, 2)).doit().evalf(4)
```




$$12.06$$




```python
# Símbolo do ifinito, digitar 2 ós.
oo
```




$$\infty$$




```python
-oo
```




$$-\infty$$



75df807ce39e83b1e0ff9d43b7cfe040b65b9572
ipynb
Jupyter Notebook
Calculo.ipynb
ascaniopy/jupyter
5544edfd3f1a1801c924f9cb58dd260282358f66
MIT
Calculo.ipynb
ascaniopy/jupyter
5544edfd3f1a1801c924f9cb58dd260282358f66
MIT
Calculo.ipynb
ascaniopy/jupyter
5544edfd3f1a1801c924f9cb58dd260282358f66
MIT
Qwen/Qwen-72B
1. YES
2. YES