WP 34S difficulty with an integration

[lrdheat]

On the WP 34S, the integral from 0 to 3 of 1/(3ROOT (3-x))^2 produces 6.6001 with an estimated accuracy of 4.3572 E-6. This on double accuracy. Wondering what in this function causes this lack of resolution when the CASIO fx-991EX produces 6.6 to full float resolution (accuracy to 9 digits). This is clearly an outlier as most WP 34S integrations are quick, and often have an accuracy of <1 E-16.

[lrdheat]

Make that from 0 to 3 of (3ROOT (3*x -1))^2

[Thomas Okken]

The function has discontinuous derivatives at 1/3, and that tends to cause numerical integration algorithms to converge slowly. If you integrate the parts from 0 to 1/3 and from 1/3 to 3 separately, you'll probably get better results.