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)
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: 2020-05-01 22:57:17 +0100
Seen: 472 times
Last updated: May 03 '20
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