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HSC 2016 MX2 Integration Marathon (archive) (2 Viewers)

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InteGrand

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Re: MX2 2016 Integration Marathon


I thought about this just now


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Edit: fraction should be +2
Nice! The last integral can be quickly dealt with using the auxiliary angle method to transform the denominator into a single sinusoid or cosinusoid. Then have fun transforming everything back in terms of x (something you'd probably feel is the last thing you'd want to do after such a long integral haha). :p
 

InteGrand

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Re: MX2 2016 Integration Marathon

Good news, LaTeX appears to be working here again. Test:
 

Paradoxica

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Re: MX2 2016 Integration Marathon

Yeah, there are a few different ways / times to do it. I don't think any of them will be significantly faster than all of the others though, its pretty much preference.
If it involves long division, for me, that's an automatic no. I avoid long division at all costs.

Here's my method:



 
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leehuan

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Re: MX2 2016 Integration Marathon

Just gonna spoil the brute method:

Expand out the double angle, u=sin(x), partial fractions.
 

omegadot

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Re: MX2 2016 Integration Marathon

I didn't think the hyperbolic functions and their inverses were part of the standard MX2 course. Am I mistaken?
 

KingOfActing

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Re: MX2 2016 Integration Marathon

I didn't think the hyperbolic functions and their inverses were part of the standard MX2 course. Am I mistaken?
We've already gone over them in my 3U class, so I don't know.
 

InteGrand

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Re: MX2 2016 Integration Marathon

I didn't think the hyperbolic functions and their inverses were part of the standard MX2 course. Am I mistaken?
You're not mistaken. Some teachers might teach it as an 'extension'.
 
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braintic

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Re: MX2 2016 Integration Marathon

I didn't think the hyperbolic functions and their inverses were part of the standard MX2 course. Am I mistaken?
They have been asked indirectly in older HSC exams, where the functions C(x) and S(x) were defined in terms of exponentials, and the various properties required to be derived.
 

leehuan

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Re: MX2 2016 Integration Marathon

They have been asked indirectly in older HSC exams, where the functions C(x) and S(x) were defined in terms of exponentials, and the various properties required to be derived.
Whilst I picked up the hint, they will forever remain indirect questions.
 

DatAtarLyfe

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Re: MX2 2016 Integration Marathon

You're not mistaken. Some teachers might teach it as an 'extension'.
IIRC, there is a question in the 3u cambridge under inverse trig that works through hyperbolic functions, not sure if it's extension...
 

InteGrand

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Re: MX2 2016 Integration Marathon

IIRC, there is a question in the 3u cambridge under inverse trig that works through hyperbolic functions, not sure if it's extension...
Yeah, there is definitely a question there about their derivatives' properties, but they don't mention that these functions are the hyperbolic functions. HSC students aren't expected to know the properties of these functions, or even what these functions are. They'd be indirect questions if asked, as leehuan said. Such questions can be done without any knowledge of the hyperbolic functions. :)
 

DatAtarLyfe

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Re: MX2 2016 Integration Marathon

oh, well my maths teacher taught us as well, he said "it's good to have knowledge of them so that you can approach questions more uniquely"
Idk he was probs high
 
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