HSC 2016 MX2 Integration Marathon (archive) (4 Viewers)

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InteGrand

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Re: MX2 2016 Integration Marathon

Part (i) reminds me of question 16b (I think?) in the 2014 HSC

Anyhow, I bags answering this Q; will post up my sol'n soon
Yeah, this question is similar to that Q., I just changed it slightly to yield the infinite sum for a different number. :) It's not too hard a Q. since it's a guided one, but I put this in mainly to give a HSC-style Q. since we haven't had one of those for a while (so we probably scared off some 2016'er lurkers :p) as well as for the infinite series.
 
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leehuan

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Re: MX2 2016 Integration Marathon

Just found it, question 7)a) from 2007.

http://www.boardofstudies.nsw.edu.au/hsc_exams/exam-papers-2007/index5.html

They give barely any guidance and it's EXACTLY what seanie posted.
By considering the first two derivatives is plenty of guidance in my eyes. Literally when I was doing that question the moment they said derivatives I was like pfft, even though I already had a fair idea on where to start with part (i).

And also what InteGrand said - those inequalities were given. True, this is a marathon, but it doesn't mean everyone can figure out everything themselves.

Furthermore, I would not have been able to infer an integral from THAT expression without being shown it as a mere MX2 student.
 

leehuan

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Re: MX2 2016 Integration Marathon

Yeah, this question is similar to that Q., I just changed it slightly to yield the infinite sum for a different number. :) It's not too hard a Q. since it's a guided one, but I put this in mainly to give a HSC-style Q. since we haven't had one of those for a while (so we probably scared off some 2016'er lurkers :p) as well as for the infinite series.
It rang a huge bell in my head.
 

seanieg89

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Re: MX2 2016 Integration Marathon

A followup from Integrand's question along the same theme:







BONUS:

 

KingOfActing

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Re: MX2 2016 Integration Marathon

Oh whoops, I forgot to show the working to get U_1. It's not hard, just solve for it in AU_0 + BU_1 = pi
 

porcupinetree

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Re: MX2 2016 Integration Marathon

Next question, one of my favourites:

 
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