Numerical Integration in Python/v3

Learn how to integrate a sequence or list of values numerically

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Imports¶

The tutorial below imports NumPy, Pandas, and SciPy.

In [1]:

import plotly.plotly as py
import plotly.graph_objs as go
from plotly.tools import FigureFactory as FF

import numpy as np
import pandas as pd
import scipy

Integrate the Sine Function¶

How to use numerical integration to find the area of $y = sin(x)$ between $0$ and $2\pi$.

In [2]:

x = np.linspace(0, 2*np.pi, 100)
y = np.sin(x)

trace1 = go.Scatter(
    x=x,
    y=y,
    mode='lines',
)

# use numpy's built in trapezoid-rule integration tool
dy = np.trapz(y, x)

annotation = go.Annotation(
    x=4.5,
    y=1.25,
    text='Numerical Integration of sin(x) is approximately %s' % (dy),
    showarrow=False
)

layout = go.Layout(
    annotations=[annotation]
)

trace_data = [trace1]
fig = go.Figure(data=trace_data, layout=layout)

py.iplot(fig, filename='1d-numerical-integration')

Out[2]: