Problem with integrate(function(x) x^3 / sin(x), -pi/2, pi/2)

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

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Problem with integrate(function(x) x^3 / sin(x), -pi/2, pi/2)

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