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

[Leonard Mada]

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