# Integrate a Chebyshev series and set the lower bound of the integral using NumPy in Python

In this article, we will see how to integrate a Chebyshev series and set the lower bound of the integral in Python using Numpy.

To perform Chebyshev integration, NumPy provides a function called chebyshev.chebint which can be used to integrate Legendre series.

Syntax: chebyshev.chebint(c, lbnd=0, scl=1, axis=0)

Parameters:

c – Array of Chebyshev series coefficients.
lbnd – The lower bound of the integral. (Default: 0)
scl – Following each integration the result is multiplied by scl before the integration constant is added. (Default: 1)
axis – Axis over which the integral is taken.

Example 1:
In the first example. let us consider a 1D array with 5 elements with a lbnd set to -2. Import the necessary packages as shown and pass the appropriate parameters as shown below. We are also displaying shape, dimensions, and data type of created numpy array.

## Python3

 `import` `numpy as np ` `from` `numpy.polynomial ``import` `chebyshev ` ` `  `# co.efficient array ` `c ``=` `np.array([``11``, ``12``, ``13``, ``14``, ``15``]) ` ` `  `print``(f``'The shape of the array is {c.shape}'``) ` `print``(f``'The dimension of the array is {c.ndim}D'``) ` `print``(f``'The datatype of the array is {c.dtype}'``) ` ` `  `res ``=` `chebyshev.chebint(c, lbnd``=``-``2``) ` ` `  `# integrated chebyshev series ` `# with  lbnd=-2 ` `print``(f``'Resultant series ---> {res}'``) `

Output:

The shape of the array is (5,)

The dimension of the array is 1D

The datatype of the array is int64

Resultant series —> [ 3.77083333e+02  4.50000000e+00 -5.00000000e-01 -3.33333333e-01

1.75000000e+00  1.50000000e+00]

Example 2:

In the first example. let us consider a 2D array with 5 elements each with a lbnd set to -1. Import the necessary packages as shown and pass the appropriate parameters as shown below. We are also displaying the shape, dimensions, and data type of created NumPy array.

## Python3

 `import` `numpy as np ` `from` `numpy.polynomial ``import` `chebyshev ` ` `  `# co.efficient array ` `c ``=` `np.array([[``11``, ``12``, ``13``, ``14``, ``15``], [``56``, ``55``, ``44``, ``678``, ``89``]]) ` ` `  `print``(f``'The shape of the array is {c.shape}'``) ` `print``(f``'The dimension of the array is {c.ndim}D'``) ` `print``(f``'The datatype of the array is {c.dtype}'``) ` ` `  `res ``=` `chebyshev.chebint(c, lbnd``=``-``1``) ` ` `  `# integrated chebyshev series ` `# with  lbnd=-1 ` `print``(f``'Resultant series ---> {res}'``) `

Output:

The shape of the array is (2, 5)

The dimension of the array is 2D

The datatype of the array is int64

Resultant series —> [[  -3.     -1.75    2.   -155.5    -7.25]

[  11.     12.     13.     14.     15.  ]

[  14.     13.75   11.    169.5    22.25]]

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