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Python | Scipy integrate.romberg() method

With the help of `scipy.integrate.romberg()` method, we can get the romberg integration of a callable function from limit a to b by using `scipy.integrate.romberg()` method.

Syntax : `scipy.integrate.romberg(func, a, b)`
Return : Return the romberg integrated value of a callable function.

Example #1 :
In this example we can see that by using `scipy.integrate.romberg()` method, we are able to get the romberg integration of a callable function from limit a to b by using `scipy.integrate.romberg()` method.

 `# import numpy and scipy.integrate``import` `numpy as np``from` `scipy ``import` `integrate``gfg ``=` `lambda` `x: np.exp(``-``x``*``*``2``)`` ` `# using scipy.integrate.romberg()``geek ``=` `integrate.romberg(gfg, ``0``, ``3``, show ``=` `True``)`` ` `print``(geek)`

Output :

```Romberg integration of <function vectorize1..vfunc at 0x00000209C3641EA0> from [0, 3]

Steps  StepSize   Results
1  3.000000  1.500185
2  1.500000  0.908191  0.710860
4  0.750000  0.886180  0.878843  0.890042
8  0.375000  0.886199  0.886206  0.886696  0.886643
16  0.187500  0.886205  0.886207  0.886207  0.886200  0.886198
32  0.093750  0.886207  0.886207  0.886207  0.886207  0.886207  0.886207
64  0.046875  0.886207  0.886207  0.886207  0.886207  0.886207  0.886207  0.886207
128  0.023438  0.886207  0.886207  0.886207  0.886207  0.886207  0.886207  0.886207  0.886207

The final result is 0.8862073482595311 after 129 function evaluations.
```

Example #2 :

 `# import numpy and scipy.integrate``import` `numpy as np``from` `scipy ``import` `integrate``gfg ``=` `lambda` `x: np.exp(``-``x``*``*``2``) ``+` `1` `/` `np.sqrt(np.pi)`` ` `# using scipy.integrate.romberg()``geek ``=` `integrate.romberg(gfg, ``1``, ``2``, show ``=` `True``)`` ` `print``(geek)`

Output :

```Romberg integration of <function vectorize1..vfunc at 0x00000209E1605400> from [1, 2]

Steps  StepSize   Results
1  1.000000  0.757287
2  0.500000  0.713438  0.698822
4  0.250000  0.702909  0.699400  0.699438
8  0.125000  0.700310  0.699444  0.699447  0.699447
16  0.062500  0.699663  0.699447  0.699447  0.699447  0.699447
32  0.031250  0.699501  0.699447  0.699447  0.699447  0.699447  0.699447

The final result is 0.6994468414978009 after 33 function evaluations.
```

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