Problem with integral on WP 34s

[Albert Chan]

(09-15-2021 02:21 AM)lrdheat Wrote:  How, then, does the WP 34S on DM 42 recognize the important part of the curve when
integrating from 0 to infinity (it converges on 1!)?

Quote:For exp-sinh, a to ∞, c = a, sample points f(c+d), then f(c+d/r), f(c+d*r)

Sorry, I missed the question.

r → ∞: (c+d/r) is approaching c, (c+d*r) to infinity. (for a to ∞, d>0)
r → 1 : (c+d/r) and (c+d*r) are both approaching (c+d)

So, exp-sinh is really summing of 2 integrals.

\( \displaystyle \int_c^∞ = \int_c^{c+d} + \int_{c+d}^∞ \)

Test using code from here (I had updated quad to return function call counts too)

lua> Q = require'quad'
lua> f = function(x) return x*exp(-x) end

For x = 0 .. inf, f(x) peaked at x=1, so default d=1 is not too bad.

lua> Q.quad(f, 0, huge) -- d = 1 (default)
0.9999999999749527 2.5934163150981393e-009 107

But, from plots, we know 0 .. 10 is where the action is.

lua> Q.quad(f, 0, huge, 10) -- d = 10
0.999999999999988 7.448208716454109e-013 61