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SciPy - integrate.quadrature() Method
The SciPy integrate.quadrature() method is used to calculate the numerical integration. In data analysis, we use this method to perform the various tasks such as calculating area under curve, evaluate the definite integral and solving differential equation.
Syntax
Following is the syntax of the SciPy integrate.quadrature() method −
quadrature(func, arg_1, arg_2)
Parameters
This function accepts the following parameters −
- func: This defines the custom function to integrate.
- arg_1: This determine the lower limit of integration interval.
- arg_2: This determine the upper limit of integration interval.
Return value
This method return the float value as result.
Example 1
Following is the SciPy integrate.quadrature() method which illutrate the simple polynomial function which is f(x) = x2 over the interval of [0, 1].
from scipy import integrate # define the function to integrate def func(x): return x**2 # perform the integration res, err = integrate.quadrature(func, 0, 1) # display the result print("Integral:", res) print("Error estimate:", err)
Output
The above code produces the following output −
Integral: 0.33333333333333337 Error estimate: 0.0
Example 2
Here, we demonstrate the trigonometric function by defining sin() function and set the inteval between 0 to pi.
In mathematics, we represent the above sentence as f(x) = sin(x) over the interval of [0, ]
import numpy as np import scipy.integrate as sp # define the function to integrate with trigonometric function def fun(x): return np.sin(x) # perform the integration res, err = sp.quadrature(fun, 0, np.pi) print("Integral:", res) print("Error estimate:", err)
Output
The above code produces the following output −
Integral: 2.0000000000017897 Error estimate: 5.245188727798222e-10
Example 3
The program demonstrate the integrate of function with extra parameter which is f(x) = a * x + b over the interval of [0, 2] where a = 3 and b = 4.
import numpy as np import scipy.integrate as sp def fun(x, a, b): return a * x + b res, err = sp.quadrature(fun, 0, 2, args=(4, 5)) print("Integral:", res) print("Error estimate:", err)
Output
The above code produces the following output −
Integral: 18.0 Error estimate: 0.0