Brain Teaser  Area enclosed by a parabola and a line

09152015, 02:59 PM
(This post was last modified: 09152015 03:21 PM by fhub.)
Post: #17




RE: Brain Teaser  Area enclosed by a parabola and a line
(09152015 01:30 PM)Gerson W. Barbosa Wrote: Franz, I'm trying to extend the problem to the biquadratic parabola (y = x^4). The expression for lines normal to it at a point P(u, u^4) was obtained from Thomas Klemm's method above.Aaah ok, but that's in fact a very complicated calculation! You get the left intersection point from the cubic equation x^3+u*x^2+u^2*x+1/(4*u^3)+u^3=0 (which is the quartic polynomial divided by (xu)), and then you have to calculate the definite integral from this complicated left point to u. And finally solve the terrible equation A'(u)=0 ... Well, I get a different result: u=0.743514881896 with A=1.22954355289 Franz 

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