Infinity And Improper Integrals


Here we show how to use sage's symbol for infinity. Because the standard symbol for infinity can't be found on a normal keyboard, sage uses oo, or two lowercase o's. For negative infinity, -oo is used. We will demonstrate with the improper integral

\begin{align} \int_{-\infty}^{\infty}e^{-x^2}dx \end{align}

Sage Cell

As you can see, the integral evaluates correctly, to $\sqrt{\pi}$


f(x) = e^(-x^2)
integrate(f(x), x, -oo, oo)




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Author: Gregory V. Bard. Sage for Undergraduates. American Mathematical Society, Providence, RI, 2015. Available at

Date: 27 Feb 2019 00:21

Submitted by: Zane Corbiere

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