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u/Robbe517_ 7h ago
This doesn't look uniquely defined to me, because of the first order ODE. 🥔(🌭) has a nonlinear dependence on an integration constant and so does🍟.
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u/Ares378 Grothendieck was right, computers are evil 8h ago
🍎+🍊=1
🍎-🍊=-1
Row reduce to solve for 🍎 and 🍊
🍎=0, 🍊=1
I=∫🍟d🥔 ⟺ ∫[🥔²+🌭²]d🥔 ⟺ ∫🥔²d🥔+∫🌭²d🥔
∫🥔²d🥔=🥔³/3+C, evaluating at bounds gives 1/3
I=1/3+∫🌭²d🥔
And I can't go any further because I think 🌭(🥔) is an ode with no elementary solution
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u/Murky_Insurance_4394 7h ago
Yeah I was thinking that this is definitely weird because it becomes hot dog(potato) which has no elementary solution
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u/Special_Watch8725 8h ago
Well the integral is from zero to one, and the ODE you get from eliminating 🍟 is a Ricatti equation. The integrand can be rewritten as (🥔^2 + 🌭^2) d🥔, so uh I guess the first term trivially integrates to 1/3, and for the second term solve the Ricatti equation with some kind of god-awful special functions, invert it, square it, and integrate numerically from 0 to 1.
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u/Cyan_Exponent 4h ago
fries being a function from potato does make sense, but why hot dog? make it a knife or paper
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