Lära Implementing Integrals in Python

Svep för att visa menyn

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: 8/3 
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

Var allt tydligt?

Tack för dina kommentarer!

Avsnitt 3. Kapitel 6

Fråga AI

Fråga vad du vill eller prova någon av de föreslagna frågorna för att starta vårt samtal

Avsnitt 3. Kapitel 6