HSC 2016 MX2 Integration Marathon (archive) (1 Viewer)

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leehuan

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I do not feel at home without this...

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Here post integrals for helping 2016 students with integration!

Do not post a question until the last one is answered

(Reference to Sy123 for the copy and paste)
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FIRST QUESTION:

 

InteGrand

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Re: MX2 2016 Integration Marathon

I do not feel at home without this...

------------------------------------------------------------
Here post integrals for helping 2016 students with integration!

Do not post a question until the last one is answered

(Reference to Sy123 for the copy and paste)
------------------------------------------------------------
FIRST QUESTION:

The 2015 one still has some unanswered ones.
 

leehuan

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Re: MX2 2016 Integration Marathon

I really couldn't be bothered doing the general case but I feel as though if I didn't treat c1=c2=0 things would've gone haywire. C3 doesn't seem as problematic though


Edit: So if we sub in the full integral and keep C3 there, our final result (using index laws) is going to be 66 * e^(C3), so we can just say the final answer is 66A for some positive arbitrary constant A.

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Paradoxica

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Re: MX2 2016 Integration Marathon

I really couldn't be bothered doing the general case but I feel as though if I didn't treat c1=c2=0 things would've gone haywire. C3 doesn't seem as problematic though


Edit: So if we sub in the full integral and keep C3 there, our final result (using index laws) is going to be 66 * e^(C3), so we can just say the final answer is 66A for some positive arbitrary constant A.

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Wolfram Alpha cannot evaluate the general case. I assume if one exists, it requires higher order functions found in real and complex analysis. So the question should be restated as...



Anyway, my solution to 1.

















 

leehuan

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Re: MX2 2016 Integration Marathon

I'll get around to treating F(n) as that definite integral later. Anyway, hopefully some (non-accelerated... :p) 2016ers will show up.

 

Paradoxica

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Re: MX2 2016 Integration Marathon

I'll get around to treating F(n) as that definite integral later. Anyway, hopefully some (non-accelerated... :p) 2016ers will show up.
Oh, the definite form is identical to assuming the constants of integration are zero. It was just me editing the problem to fit your solution.

Technically I'm not accelerated so....





The rest is done by substitution, yielding

 

Paradoxica

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Re: MX2 2016 Integration Marathon

Are you doing your hsc in 2016, but have been tutored a year ahead?
The tutoring helps with content digestion, but not with problem solving skills. I almost exclusively never use any of Truong's techniques. And if I do, that's because I see no other way, or am unaware of it.
 

DatAtarLyfe

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Re: MX2 2016 Integration Marathon

Apart from the accelerated kids, pretty much none of us are up to integration, so hoping that some of the 2016ers will answer is a little ambitious (unless of course some it's just harder 3u)
 

Sien

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Re: MX2 2016 Integration Marathon

Apart from the accelerated kids, pretty much none of us are up to integration, so hoping that some of the 2016ers will answer is a little ambitious (unless of course some it's just harder 3u)
Integration is just backwards differentiation
Edit: crap didn't realise this was mx2 territory

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leehuan

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Re: MX2 2016 Integration Marathon

I'm trying to keep the difficulty low for now. I'll increase it in February.



Most of these integrals should be doable with textbook browsing.
 

KingOfActing

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Re: MX2 2016 Integration Marathon

I'm trying to keep the difficulty low for now. I'll increase it in February.



Most of these integrals should be doable with textbook browsing.


NEXT QUESTION:
 
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Sy123

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Re: MX2 2016 Integration Marathon



 

outlier1

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Re: MX2 2016 Integration Marathon

The tutoring helps with content digestion, but not with problem solving skills. I almost exclusively never use any of Truong's techniques. And if I do, that's because I see no other way, or am unaware of it.
What's your opinion and rate on Truong's tutoring? Everyone says they're the best
 

Sy123

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Re: MX2 2016 Integration Marathon

why must you taunt me?



Not intentional haha

That substitution requires a constant in front of it, otherwise we can't simplify it to eliminate the square-root
 

Paradoxica

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Re: MX2 2016 Integration Marathon

What's your opinion and rate on Truong's tutoring? Everyone says they're the best
It's good if you're not willing to put the work to understand the syllabus content for mathematics, since he makes a lot of things one-size fits all techniques. This doesn't really help me though, as I consider everything on a case-by-case basis.
 
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