Fractional Part - A Difficult Integral

[Gerald H]

Here some results for integrating FP from zero to 5.8:


Maple V Release 3.0

evalf(int(frac(x), x=0..5.8)) 2.820001887

Maxima 5.23.2

quad_qags(x-floor(x), x, 0, 5.8) [2.720000001263673,1.5265947617137954*10^-
8,3171,0]

PARI 2.4.2

intnum(x=0,5.8,frac(x)) 2.770657207613055496607250297

WolframAlpha 2011-5-28

integrate(frac(x),x,0,5.8) 2.82

CASIO fx-9860GII (& fx-5800P)

∫_0^5.8▒〖Frac X〗 dx 2.72

HP 42S

Gauss-Lagrange 16 point:

Divisions: 1 2.32
2 2.71441362769
3 2.95110930932
4 2.84122268726
5 2.72066778956
6 2.8405122545

HP 50G

Inbuilt integration programme: ∫_0^5.8▒〖FP(X)〗 dX

FIX 6 2.820116 in 1,232.15 seconds

Gauss-Lobatto 4 point formula with 7 and 13 point Kronrod extensions:

FIX 2 2.80
3 2.819
4 2.8199
5 2.82000
6 2.820000 in 12.34 seconds





SHARP EL-9650

∫_0^5.8▒〖fpart X〗 dxX 2.419454779

TI-84 Plus 2.53MP

fnInt(fPart(X),X,0,5.8) 2.720014333

TI-86 (tol = 1E-5)

fnInt(fPart x,x,0,5.8) 2.71992436738

TI-89 (& voyage 200 & 92(plus))

∫_0^5.8▒〖fPart (x)〗 dx 2.72000000036