Oppiskele 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`?

Oliko kaikki selvää?

Kiitos palautteestasi!

Osio 3. Luku 6

Kysy tekoälyä

Kysy mitä tahansa tai kokeile jotakin ehdotetuista kysymyksistä aloittaaksesi keskustelumme

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?

Pyyhkäise näyttääksesi valikon

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`?

Oliko kaikki selvää?

Kiitos palautteestasi!

Osio 3. Luku 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`?