Using C47 sim, which uses the same integration code from WP43, the EQN method of integrating the same formula renders exactly the same result, to all decimals quoted up here. I do not profess to know the answer here.BINUBALL wrote: ↑Sat Mar 25, 2023 3:43 pmIntegration accuracy issue. I'm using version 0.23.9 windows simulator.
∫ x(sin x+cos x+1) dx from 0 to 10^3
LBL 'f(x)'
MVAR 'x'
RCL 'x'
sin
RCL 'x'
cos
+
1
+
RCL 'x'
×
END
ACC: 1e-9, ↓Lim:0, ↑Lim: 1e3
WP43 gives 483662.530…, where correct value is about 500264.890…. An upper limit of integral's uncertainty(stack register Y) is 435276.691…. Surprisingly big compared to integration of the same function from 0 to 10^2.(which is 1.923e-16)
However, this formula illustrates another unexpected (for me as the author) graphing result: aliasing! Due to the limited number of x-steps of the graph and the extreme number of oscillations in between those x-steps and due to pot luck of how close multiples of the oscillation period (\(2pi\)) are to the regular distance between x-steps of the graph, you may actually see no change in the graph, or some weird stuff not representative of the function, see below:
. Impossible graphing result from \(x = 0\) to \(1000\).
There are many ways to prove the aliasing, in this case simply shift the graph range to: \(x = \pi/2\) to \(1000-\pi/2\):
. This of course still is wrong as a quick look at the range of \(x = 500\) to \(500+12\pi\) shows:
.