# Numerical Integration in Python/v3

Learn how to integrate a sequence or list of values numerically

See our Version 4 Migration Guide for information about how to upgrade.

#### New to Plotly?¶

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#### Imports¶

The tutorial below imports NumPy, Pandas, and SciPy.

In :
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 :
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: 