Sharp EL-W506T vs. Sharp EL-W516T

[Albert Chan]

(01-31-2020 12:21 AM)Mjim Wrote:  I thought I would try an even steeper exponential to see what would happen:
r = e^(x^2) -> dr = 2xe^(x^2) dx

integral(C/r^2, a, b) = integral(2Cx/e^(x^2), sqrt[ln(a)], sqrt[ln(b)] )

How about shifting the curve, for any integrand, say f(x)

\(\int _a ^b f(x) dx = \int _1 ^{b-a+1} f(y + (a-1)) dy = \int _0 ^{\log(b-a+1)} f(e^z + (a-1)) e^z dz \)

XCas> [a, b, c] := [6.371e6, 9.4607304725808e15, 3.98589196e17]
XCas> f(r) := c/r^2
XCas> integrate(f(e^z + (a-1)) * e^z, z = 0 .. log(b-a+1))         → 62563050656.3

Try plotting this. It look like normal distribution curve !

Code:

n       simpsons
2       88521044629
4       23319253438
8       55920947081
16      66807272619
32      62510235388
64      62563085106
128     62563050656
256     62563050656
512     62563050656
1024    62563050656