Brain Teaser  Area enclosed by a parabola and a line

09182015, 05:51 PM
Post: #28




RE: Brain Teaser  Area enclosed by a parabola and a line
Just for the record, here are some numerical results for the cases y=x^4, y=6 and y=8. Notice the minimum areas occur for normal lines passing near y(3/4), y(5/6) and y(7/8), respectively. The values of u for minimum areas should be accurate to 7 or 8 digits.
y=x^4 u: 0.730000000000 Area: 1.232203807010 u: 0.740000000000 Area: 1.229721793524 u: 0.741869418802 Area: 1.229582549556 u: 0.743490000000 Area: 1.229543561785 u: 0.743514882370 Area: 1.229543552881 u: 0.743515349953 Area: 1.229543552884 u: 0.743543197140 Area: 1.229543564411 u: 0.744136760955 Area: 1.229549111764 u: 0.75000000000o Area: 1.230145031369 y=x^6 u: 0.810000000000 Area: 1.120523733964 u: 0.814713174965 Area: 1.119930602299 u: 0.814723174965 Area: 1.119930598819 u: 0.814724747205 Area: 1.119930598753 u: 0.814733174965 Area: 1.119930600634 u: 0.815000000000 Area: 1.119932604732 u: 0.820000000000 Area: 1.120664993006 y=x^8 u: 0.86790000000 Area: 1.24466886334 u: 0.86800000000 Area: 1.24466861630 u: 0.86796579708 Area: 1.24466859303 u: 0.86797579708 Area: 1.24466858824 u: 0.86798579708 Area: 1.24466859303 u: 0.86804996475 Area: 1.24466885164 u: 0.86810000000 Area: 1.24466932686 Gerson. 

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