`subdivisions` is the maximum number of subintervals. Looking here https://github.com/wch/r-source/blob/79298c499218846d14500255efd622b5021c10ec/src/appl/integrate.c#L1275 I'm not surprised that changing `subdivisions` has no effect on the outcome. The integration method from {pracma} might work, maybe it never calculates the function at 0, maybe it's using some alternate method. Or maybe it did calculate f(0) and got NaN and just assumed that the limit converged. Maybe that's a fair assumption, and maybe it's not. However: integrate(function(x) ifelse(x == 0, 0, x^3/sin(x), -pi/2, pi/2) works perfectly fine and is a better function definition anyway. `integrate` in the {stats} package is unlikely to change, so use the alternate function definition or use {pracma}.
On Sat, Jan 7, 2023 at 10:41 PM Leonard Mada <leo.mada at syonic.eu> wrote:
Dear Andrew, The limit when x approaches 0 is 0. I think most integration algorithms handle this situation. This actually works, and it "includes" formally the point x = 0: integrate(function(x) x^3 / sin(x), -pi/2, pi/2 + 1E-10) Trying to "bypass" the 0 using subdivisions unfortunately did not work: integrate(function(x) x^3 / sin(x), -pi/2, pi/2, subdivisions=4097) # or 4096 Sincerely, Leonard On 1/8/2023 5:32 AM, Andrew Simmons wrote: 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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