Working with scipy.integrate

The scipy.integrate module provides functions for numerical integration and solving ordinary differential equations (ODEs).
It’s useful when:

• You need to evaluate a definite integral
• You want to integrate functions without an exact formula
• You are solving systems of ODEs

Importing the required modules:

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import numpy as np
from scipy import integrate

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# Integrand
f = lambda x: np.sin(x)

# Integrate from 0 to π
val, err = integrate.quad(f, 0, np.pi)

print("Integral value:", val)
print("Estimated error:", err)

Here:

• quad returns the integral value and an error estimate
• This is useful for smooth, well-behaved functions

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# Derivative function
def dydt(t, y):
    return -2 * y

# Time span and evaluation points
t_span = (0, 3)
t_eval = np.linspace(*t_span, 100)

# Solve the ODE
sol = integrate.solve_ivp(dydt, t_span, y0=[1.0], t_eval=t_eval)

print("First 5 y values:", sol.y[0][:5])

Here:

• solve_ivp solves initial value problems for ODEs
• t_span is the interval of integration
• y0 is the initial condition

• quad() — integrates single-variable functions over a given range.
• solve_ivp() — solves initial value problems for differential equations.
• Use NumPy for defining functions and arrays to ensure compatibility with SciPy’s integration routines.

In the next lesson, we’ll look at Signal and Image Processing Modules in SciPy.