Brain Teaser - Area enclosed by a parabola and a line
09-21-2015, 09:48 PM (This post was last modified: 09-21-2015 09:53 PM by Gerson W. Barbosa.)
Post: #32
 Gerson W. Barbosa Senior Member Posts: 1,452 Joined: Dec 2013
RE: Brain Teaser - Area enclosed by a parabola and a line
(09-21-2015 05:53 PM)fhub Wrote:
(09-18-2015 05:51 PM)Gerson W. Barbosa Wrote:  y=x^4
u: 0.743514882370 Area: 1.229543552881

y=x^6
u: 0.814724747205 Area: 1.119930598753

y=x^8
u: 0.86797579708 Area: 1.24466858824

... your Area result for x^8 looked rather illogical for me (IMO the area should continuously decrease for higher exponents n) ...

The following might have been closer if my function Y had been Y := u*u*u*u*u*u*u*u - (x-u)/(8*u*u*u*u*u*u*u) - x*x*x*x*x*x*x*x rather than Y := u*u*u*u*u*u*u*u - (x-u)/(6*u*u*u*u*u*u*u) - x*x*x*x*x*x*x*x. In FreePascal the yellow is brighter and the blue is fainter, but this is not an excuse as I ought to have mistrusted the increase in the area.

y=x^8

u: 0.840000000000 Area: 1.038962719953
u: 0.849000000000 Area: 1.034585573337
u: 0.849999511578 Area: 1.034517355546
u: 0.850000000000 Area: 1.034517342489
u: 0.850322146435 Area: 1.034513041971
u: 0.851000000000 Area: 1.034532095727
u: 0.860000000000 Area: 1.038377424828
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 Messages In This Thread Brain Teaser - Area enclosed by a parabola and a line - CR Haeger - 09-11-2015, 04:57 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-13-2015, 12:17 AM RE: Brain Teaser - Area enclosed by a parabola and a line - CR Haeger - 09-13-2015, 01:19 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Claudio L. - 09-13-2015, 01:35 AM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-13-2015, 02:40 AM RE: Brain Teaser - Area enclosed by a parabola and a line - Thomas Klemm - 09-13-2015, 04:23 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-15-2015, 03:29 AM RE: Brain Teaser - Area enclosed by a parabola and a line - fhub - 09-15-2015, 11:56 AM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-15-2015, 01:30 PM RE: Brain Teaser - Area enclosed by a parabola and a line - fhub - 09-15-2015, 02:59 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-15-2015, 04:18 PM RE: Brain Teaser - Area enclosed by a parabola and a line - fhub - 09-15-2015, 05:00 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-15-2015, 05:08 PM RE: Brain Teaser - Area enclosed by a parabola and a line - fhub - 09-15-2015, 09:42 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Bunuel66 - 09-13-2015, 10:06 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-16-2015, 02:19 AM RE: Brain Teaser - Area enclosed by a parabola and a line - CR Haeger - 09-14-2015, 03:57 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Bunuel66 - 09-14-2015, 05:08 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Bunuel66 - 09-14-2015, 05:51 PM RE: Brain Teaser - Area enclosed by a parabola and a line - eried - 09-14-2015, 08:32 PM RE: Brain Teaser - Area enclosed by a parabola and a line - CR Haeger - 09-14-2015, 10:06 PM RE: Brain Teaser - Area enclosed by a parabola and a line - CR Haeger - 09-15-2015, 02:44 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-16-2015, 02:06 AM RE: Brain Teaser - Area enclosed by a parabola and a line - Thomas Klemm - 09-16-2015, 05:12 AM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-16-2015, 03:09 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Thomas Klemm - 09-16-2015, 03:55 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-16-2015, 04:14 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-18-2015, 05:51 PM RE: Brain Teaser - Area enclosed by a parabola and a line - fhub - 09-21-2015, 05:53 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-21-2015, 06:40 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Gerson W. Barbosa - 09-21-2015 09:48 PM RE: Brain Teaser - Area enclosed by a parabola and a line - Thomas Klemm - 09-18-2015, 08:20 PM

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