SciPy — Integration

Quad (single integral)

from scipy.integrate import quad

def f(x):
    return x**2

result, error = quad(f, 0, 1)
print(f"Integral = {result:.4f}")
print(f"Error = {error:.2e}")

Definite integral

import numpy as np

# Integrate sin(x) from 0 to pi
result, _ = quad(np.sin, 0, np.pi)
print(f"Integral of sin(x) from 0 to pi = {result:.4f}")

Double integral

from scipy.integrate import dblquad

def f(y, x):
    return x * y

result, error = dblquad(f, 0, 1, 0, 1)
print(f"Double integral = {result:.4f}")

Triple integral

from scipy.integrate import tplquad

def f(z, y, x):
    return x * y * z

result, error = tplquad(f, 0, 1, 0, 1, 0, 1)
print(f"Triple integral = {result:.4f}")

Numerical integration (fixed-sample)

from scipy.integrate import simps
import numpy as np

x = np.array([0, 1, 2, 3, 4])
y = np.array([0, 1, 4, 9, 16])

result = simps(y, x)
print(f"Simpson's rule = {result:.4f}")

ODE integration

from scipy.integrate import odeint

def model(y, t):
    return -2 * y

y0 = 1
t = np.linspace(0, 5, 100)
solution = odeint(model, y0, t)

Mini Practice

1. Compute a definite integral
2. Perform double integration
3. Use Simpson's rule
4. Solve a simple ODE

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Continue with Differentiation - Numerical derivatives.