Вивчайте Implementing Integrals in Python

Integration is the process of summing infinitely small parts to find the total accumulation of a function over a range. In Python, we use sympy to compute integrals symbolically.

Computing an Indefinite Integral (Antiderivative)

An indefinite integral represents the antiderivative of a function. It finds the general form of a function whose derivative gives the original function.


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import sympy as sp

# Define function
x = sp.Symbol('x')
f = x**2 

# Compute indefinite integral
F = sp.integrate(f, x) 

# Output: x**3 / 3 
print(F)

Computing a Definite Integral (Area Under Curve)

A definite integral finds the accumulated sum of a function over a range $[a,b]$ .


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import sympy as sp

# Define function
x = sp.Symbol('x')
f = x**2 

# Define integration limits
a, b = 0, 2

# Compute definite integral
integral_value = sp.integrate(f, (x, a, b)) 

# Output: 4/3 * (2^3 - 0^3) = 4 
print(integral_value)

Common Integrals in Python

Python allows us to compute common mathematical integrals symbolically. Here are a few examples:


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import sympy as sp

# Define function
x = sp.Symbol('x')

# Exponential integral
exp_integral = sp.integrate(sp.exp(x), x)  

# Sigmoid function integral
sigmoid_integral = sp.integrate(1 / (1 + sp.exp(-x)), x)  

# Quadratic function integral
quadratic_integral = sp.integrate(2*x, (x, 0, 2))

# Print results
print(exp_integral)          # Output: e^x  
print(sigmoid_integral)      # Output: log(1 + e^x)
print(quadratic_integral)    # Output: 4

1. What is the result of this integral?

2. What happens when you integrate a constant, such as `5`?

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Секція 3. Розділ 6

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Запитайте про що завгодно або спробуйте одне із запропонованих запитань, щоб почати наш чат

Suggested prompts:

Can you explain the difference between definite and indefinite integrals?

How does the `sympy` library compute integrals symbolically in Python?

Can you walk me through the code examples step by step?

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Integration is the process of summing infinitely small parts to find the total accumulation of a function over a range. In Python, we use sympy to compute integrals symbolically.

Computing an Indefinite Integral (Antiderivative)

An indefinite integral represents the antiderivative of a function. It finds the general form of a function whose derivative gives the original function.


              1234567891011
            
import sympy as sp

# Define function
x = sp.Symbol('x')
f = x**2 

# Compute indefinite integral
F = sp.integrate(f, x) 

# Output: x**3 / 3 
print(F)

Computing a Definite Integral (Area Under Curve)

A definite integral finds the accumulated sum of a function over a range $[a,b]$ .


              1234567891011121314
            
import sympy as sp

# Define function
x = sp.Symbol('x')
f = x**2 

# Define integration limits
a, b = 0, 2

# Compute definite integral
integral_value = sp.integrate(f, (x, a, b)) 

# Output: 4/3 * (2^3 - 0^3) = 4 
print(integral_value)

Common Integrals in Python

Python allows us to compute common mathematical integrals symbolically. Here are a few examples:


              123456789101112131415161718
            
import sympy as sp

# Define function
x = sp.Symbol('x')

# Exponential integral
exp_integral = sp.integrate(sp.exp(x), x)  

# Sigmoid function integral
sigmoid_integral = sp.integrate(1 / (1 + sp.exp(-x)), x)  

# Quadratic function integral
quadratic_integral = sp.integrate(2*x, (x, 0, 2))

# Print results
print(exp_integral)          # Output: e^x  
print(sigmoid_integral)      # Output: log(1 + e^x)
print(quadratic_integral)    # Output: 4

1. What is the result of this integral?

2. What happens when you integrate a constant, such as `5`?

Все було зрозуміло?

Дякуємо за ваш відгук!

Секція 3. Розділ 6

Implementing Integrals in Python

Computing an Indefinite Integral (Antiderivative)

Computing a Definite Integral (Area Under Curve)

Common Integrals in Python

1. What is the result of this integral?

2. What happens when you integrate a constant, such as 5?

Awesome!

Implementing Integrals in Python

Computing an Indefinite Integral (Antiderivative)

Computing a Definite Integral (Area Under Curve)

Common Integrals in Python

1. What is the result of this integral?

2. What happens when you integrate a constant, such as 5?

2. What happens when you integrate a constant, such as `5`?

2. What happens when you integrate a constant, such as `5`?