# 
## Overview

The `scipy.integrate.quadrature()` method in Python computes a definite integral using the numerical integration method of the [fixed-tolerance Gaussian quadrature](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.quadrature.html). The method takes a Python function, limits of integration, and absolute tolerance value as arguments and calculates the definite integral using the Gaussian quadrature.


# 
## Syntax

The function prototype is as follows:


scipy.integrate.quadrature(func, a, b, args = (), 
                           tol = 1.49e-08, 
                           rtol = 1.49e-08, 
                           maxiter = 50, 
                           vec_func = True, 
                           miniter = 1)

# 
#  Parameters

* `func`: This is the Python function or the method that is being integrated.

* `a`: This is a float value that specifies the lower limit of integration.

* `args`: This is an optional `tuple` parameter. It specifies the extra arguments to be passed to the `func` function.

* `tol, rtol`: This is an optional float value that defines the absolute tolerance. 

  > **Note:** Iteration stops when the error between the last two iterates is less than `tol` or the relative change is less than `rtol`. Its default value is `1.49e-08`.

* `maxiter`: This is an optional int value that specifies the maximum order of the Gaussian quadrature.

* `miniter`: This is an optional int value that specifies the minimum order of the Gaussian quadrature.

* `vec_func`: This is an optional bool value that specifies `True` or `False`, if `func` handles arrays as arguments. The default value is `True`.

##
## Return value

* `val`: This float value computes the Gaussian quadrature approximation to the integral within the absolute tolerance.

* `err`: This float value tells the difference between the last two estimates of the integral.

## Code

from scipy import integrate
import numpy as np

print(integrate.quadrature(np.sin, 0.0, np.pi/4))

# 
## Explanation 

- Line 1–2: We import the required libraries.

- Line 4: We use the sine function, `np.sin`, from the NumPy library and pass it to the `integrate.quadrature` method. The method integrates it using the Gaussian quadrature method with integration limits from $0$ to $\pi/4$.

What is the scipy.integrate.quadrature() method in Python?

Computes definite integrals using Gaussian quadrature, requiring function, integration limits, and tolerance.