R help - Jan 2023 - Problem with integrate(function(x) x^3 / sin(x), -pi/2, pi/2)

Dear List-Members,

I encounter a problem while trying to integrate the following function:

integrate(function(x) x^3 / sin(x), -pi/2, pi/2)
# Error in integrate(function(x) x^3/sin(x), -pi/2, pi/2) :
#? non-finite function value

# the value should be finite:
curve(x^3 / sin(x), -pi/2, pi/2)
integrate(function(x) x^3 / sin(x), -pi/2, 0)
integrate(function(x) x^3 / sin(x), 0, pi/2)
# but this does NOT work:
integrate(function(x) x^3 / sin(x), -pi/2, pi/2, subdivisions=4096)
integrate(function(x) x^3 / sin(x), -pi/2, pi/2, subdivisions=4097)
# works:
integrate(function(x) x^3 / sin(x), -pi/2, pi/2 + 1E-10)


# Note: works directly with other packages

pracma::integral(function(x) x^3 / sin(x), -pi/2, pi/2 )
# 3.385985


I hope that integrate() gets improved in base R as well.


Sincerely,


Leonard

You're dividing 0 by 0, giving you NaN, perhaps you should try

function(x) ifelse(x == 0, 0, x^3/sin(x))

On Sat, Jan 7, 2023, 22:24 Leonard Mada via R-help <r-help at
r-project.org>
wrote:
> Dear List-Members,
>
> I encounter a problem while trying to integrate the following function:
>
> integrate(function(x) x^3 / sin(x), -pi/2, pi/2)
> # Error in integrate(function(x) x^3/sin(x), -pi/2, pi/2) :
> #  non-finite function value
>
> # the value should be finite:
> curve(x^3 / sin(x), -pi/2, pi/2)
> integrate(function(x) x^3 / sin(x), -pi/2, 0)
> integrate(function(x) x^3 / sin(x), 0, pi/2)
> # but this does NOT work:
> integrate(function(x) x^3 / sin(x), -pi/2, pi/2, subdivisions=4096)
> integrate(function(x) x^3 / sin(x), -pi/2, pi/2, subdivisions=4097)
> # works:
> integrate(function(x) x^3 / sin(x), -pi/2, pi/2 + 1E-10)
>
>
> # Note: works directly with other packages
>
> pracma::integral(function(x) x^3 / sin(x), -pi/2, pi/2 )
> # 3.385985
>
>
> I hope that integrate() gets improved in base R as well.
>
>
> Sincerely,
>
>
> Leonard
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
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> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
	[[alternative HTML version deleted]]

On Sun, 8 Jan 2023 05:24:05 +0200
Leonard Mada via R-help <r-help at r-project.org> wrote:
> pracma::integral(function(x) x^3 / sin(x), -pi/2, pi/2 )
> # 3.385985
Note that at least one implementation used by pracma::integral has the
same problem:

pracma::integral(function(x) x^3/sin(x), -pi/2, pi/2, no_intervals=7)
# [1] NaN
# Warning:
# In .gkadpt(f, a, b, tol = tol) : Infinite or NA function value
# encountered.

You just have to be less lucky to have it evaluate the function at 0.
By default, the subdivision strategy used by pracma::integral combined
with the default number of intervals leaves the special point on the
edge of the interval, where the function happens not to be evaluated.

-- 
Best regards,
Ivan