How to write and evaluate definite integrals (in Python, using SymPy)

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Task

The area under a curve can be computed using a definite integral. To compute the area above the $x$ axis and under $f(x)$, from $x=a$ to $x=b$, we write

How can we write and evaluate definite integrals using software?

Related tasks:

• How to compute the derivative of a function
• How to write and evaluate indefinite integrals
• How to write and evaluate Riemann sums

Solution

This answer assumes you have imported SymPy as follows.

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from sympy import *                   # load all math functions
init_printing( use_latex='mathjax' )  # use pretty math output

Let’s compute the area under $\sin x$ from $x=0$ to $x=\pi$.

We use the same technique as in how to write and evaluate indefinite integrals, except that we add the lower and upper bounds together with $x$, as shown below.

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var( 'x' )
formula = sin(x)
Integral( formula, (x,0,pi) )

${\displaystyle \underset{0}{\overset{\pi }{\int }}\sin \left(x\right)dx}$

The above code just displays the definite integral. To evaluate it, use the integrate command.

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integrate( formula, (x,0,pi) )

${\displaystyle 2}$

Content last modified on 24 July 2023.

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Contributed by Nathan Carter (ncarter@bentley.edu)