The integral from 0 to 1 of 3Root(1-x^7) - 7Root(1-x^3) hangs the G2, requiring a reset. The virtual unit gives a warning message, pressing enter returns original integral (which one can then ~ans). Virtual and G2 work in Home...almost produce the correct answer of zero.
(03-29-2020 06:38 PM)lrdheat Wrote: [ -> ]The integral from 0 to 1 of 3Root(1-x^7) - 7Root(1-x^3) ... correct answer of zero.
Last month, we had a thread about
Wallis' product exploration.
Googled "wallis product", I found this:
Mathematical Analysis and the Mathematics of Computation, p.404, eqn. 7.87
\(\Large {1 \over \int_0^1 (1-x^{1/p})^q\;dx} = \binom{p+q}{p} = \binom{p+q}{q} = {1 \over \int_0^1 (1-x^{1/q})^p\;dx} \)
This explained why your integral had area of zero.
P.S. I do not know how above is derived. Any insight is appreciated.
(03-29-2020 09:56 PM)Albert Chan Wrote: [ -> ] (03-29-2020 06:38 PM)lrdheat Wrote: [ -> ]The integral from 0 to 1 of 3Root(1-x^7) - 7Root(1-x^3) ... correct answer of zero.
Last month, we had a thread about Wallis' product exploration.
Googled "wallis product", I found this: Mathematical Analysis and the Mathematics of Computation, p.404, eqn. 7.87
\(\Large {1 \over \int_0^1 (1-x^{1/p})^q\;dx} = \binom{p+q}{p} = \binom{p+q}{q} = {1 \over \int_0^1 (1-x^{1/q})^p\;dx} \)
This explained why your integral had area of zero.
P.S. I do not know how above is derived. Any insight is appreciated.
The G2 shouldn't crash over it, though.
My G2 didn't crash; it behaved exactly like the simulator. Perhaps you have x defined somewhere?