Python Scipy `scipy.integrate.quad()` method evaluates the integration of a given function in between the provided lower and upper limits.

## Syntax of `scipy.integrate.quad()`:

``````scipy.integrate.quad(func,
a,
b)
``````

### Parameters

`func` It is the function whose definite integral is to be calculated.
`a` Lower limit. Integration of function will start from here. It takes float value.
`b` Upper limit. Integration of function will stop here. It takes a float value.

## Return

It returns a tuple of two values :

1. Value of integral.
2. Estimate error of the integral in between actual and approximate value.

## Example Codes : `scipy.integrate.quad()` Method to Find Integral

``````import numpy as np
import scipy

def func(x):
return x

print("The result of the integration of func from 0 to 4 is: " +str(integral))
print("The error value in the integration is:" +str(error))
``````

Output:

``````The result of the integration of func from 0 to 4 is: 8.0
The error value in the integration is:8.881784197001252e-14
``````

Here, a function named `func` is created, which is simply a linear function that returns the input value without any modification. When the `scipy.integrate.quad()` method is called, `func` is integrated between lower bound `0` and upper bound `4`, and we get a tuple of 2 values as an output from the method. The first value represents the value of the definite integral, while the second value represents the error while estimating the integral.

## Calculating Integral of Cosine Using `scipy.integrate.quad()`

``````import numpy as np
import scipy

lower_bound = 0
upper_bound = np.pi / 2

def func(x):
return np.cos(x)

print ("Integral value of cosine function from 0 to pi/2 is:" + str(value))
print ("Estimated error is: " + str(err))

``````

Output:

``````Integral value of cosine function from 0 to pi/2 is: 0.9999999999999999
Estimated error is: 1.1102230246251564e-14
``````

Here, `cos(x)` is integrated in between limits `0` and `np.pi/2`. The `func` function is created that returns `cos(x)`, which is passed into the `quad` method along with upper and lower interval limits, finally producing respective integral value and absolute error.

Several other optional parameters can be used to tune the output.

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