Dear Maple Primes,
could you, please, help me with numeric integration? I’m new in numeric integration and can’t reach desired precision of a result.
Here is the integral f(xmax) that I try to compute for different values of xmax from the interval 0.025..0.24 :
where x0 is lower limit of outer integral, x0 := 0.025
and K, F and G are functions of x
a1:=8e3; a2:=6e4; a3:=3e4; a4:=1.8e8;
b1:=9.2e17; b2:=1.1e18; b3:=4.6e21;
c1:=8.202046; c2:=-12.31377; c3:=-818043.42;
Please, notice, that G (as well as G*F) is a steeply decreasing function on the interval x = 0.025..0.24.
I get "a seemingly correct" result (that means that f increases as xmax intreases), when I try to plot f(xmax) for the following "guessed" options
What is puzzling me is that I get a different "seemingly correct" result, when I modify the integral f by,
at fist, multiplying G by a constant (for example Const:=1e20; G:=Const*exp(c1+c2*x+c3*x7) )
and, second, plotting the f divided by this constant:
The following Figure presents the values of f plotted versus xmax with (red curve) and without (black curve) using of the constant Const:
Dear Primes, could you, please, comment on this difference? Because the only indicator that I have (from the analysis of G, F and K) is that f must be a monotonically (and stricktly) increasing function of xmax.
Please, find the maple worksheet in attachment.
Thank you in advance!