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Integral hangs G2
03-30-2020, 12:16 AM
Post: #3
RE: Integral hangs G2
(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.

Tom L
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Messages In This Thread
Integral hangs G2 - lrdheat - 03-29-2020, 06:38 PM
RE: Integral hangs G2 - Albert Chan - 03-29-2020, 09:56 PM
RE: Integral hangs G2 - toml_12953 - 03-30-2020 12:16 AM
RE: Integral hangs G2 - Albert Chan - 03-30-2020, 05:16 PM
RE: Integral hangs G2 - roadrunner - 03-30-2020, 12:27 AM



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