When I try something like
integral_numerical(bessel_I(0, x), (x, 0, 1))I get
TypeError: Cannot evaluate symbolic expression to a numeric value.So my question is: how to integrate numerically special functions?
According to the documentation of integral_numerical, the correct syntax is:
sage: integral_numerical(bessel_I(0,x), 0, 1)
(1.0865210970235897, 1.206280738656573e-14)Thank you! This answers my question. I have to read the documentation more carefully
Using a lambda function also works:
sage: integral_numerical(lambda x: bessel_I(0, x), (0, 1))
(1.0865210970235897, 1.206280738656573e-14)Besides numerical integration, lambda functions are often helpful for plotting.
In addition to integral_numerical, it is possible to use the nintegrate method:
sage: bessel_I(0,x).nintegrate(x, 0, 1)
(1.08652109702359, 1.206280738656574e-14, 21, 0)The output provides the value of the integral, an error estimate, the times that the function is evaluated and an error code (0 means "no problem encountered"). Write
sage: sage.calculus.calculus.nintegral?for more information.
Asked: 4 years ago
Seen: 363 times
Last updated: May 03 '20
Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.