HSC 2016 Maths Marathon (archive) (2 Viewers)

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Paradoxica

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Re: This question is 2U level difficulty, right?

Instead of integrating to find the area of the parabolic segment, you could instead use Simpson's Rule on the abscissae of P,Q,R to determine the exact area of the parabolic segment (on the appropriate function, of course)
 
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leehuan

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Re: HSC 2016 2U Marathon

Hence show that for quadratics and cubics, the approximation is exact.
Lol I was going to do that but... Didn't want to give them a bit too much


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Bestintheworld

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Re: HSC 2016 2U Marathon



took me 5 mins to write in LaTex :p
 
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Nailgun

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Re: This question is 2U level difficulty, right?

HOLY CRAP I DID IT

only took 11 days lol

I realised I used the wrong function twice when I was working out the area of the triangle

legit gna write up the entire thing now ahahah

rip half yearly study
 

leehuan

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Re: HSC 2016 2U Marathon



The proof is soundly difficult, so hints will be provided if left unanswered.
Draw any arbitrary parabola through three conveniently chosen points
 

Nailgun

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Re: HSC 2016 2U Marathon

btw is there like a notation for trapezoidal rule/simpsons?

i wanted to show what area i was trying to find with which bounds but idk how to like, write that
is what i did with the integral sign incorrect? the logic is a bit dodgy in my answer lol

edit: hey my answer was my 1000th post ahahaha
not a bad post for a milestone
 
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