Brain Teaser - Area enclosed by a parabola and a line

[Gerson W. Barbosa]

(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