HSC 2016 MX2 Integration Marathon (archive) (3 Viewers)

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leehuan

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Re: MX2 2016 Integration Marathon

NEXT QUESTION:
You question skippers

So let's just clarify briefly that for this one, find the integral of e^(x)sin(x) and e^(x)cos(x) first using a 'loopy' integration by parts. Then, we use integration by parts on the given integral, treating x as the expression to be differentiated, then sub in our results immediately earlier.
 

leehuan

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Re: MX2 2016 Integration Marathon

 

Paradoxica

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Re: MX2 2016 Integration Marathon

You question skippers

So let's just clarify briefly that for this one, find the integral of e^(x)sin(x) and e^(x)cos(x) first using a 'loopy' integration by parts. Then, we use integration by parts on the given integral, treating x as the expression to be differentiated, then sub in our results immediately earlier.
Personally, I would differentiate those instead of integrating them. Then add/subtract them together to yield the desired integral. Such is the elegance of periodic functions.
 

glittergal96

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Re: MX2 2016 Integration Marathon

Such is the elegance of periodic functions.
That example doesn't really have anything to do with periodicity.

It so happens that the functions sin(x) and cos(x) are periodic, but this property is pretty irrelevant to that integration.
 

Paradoxica

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Re: MX2 2016 Integration Marathon

That example doesn't really have anything to do with periodicity.

It so happens that the functions sin(x) and cos(x) are periodic, but this property is pretty irrelevant to that integration.
:rolleyes:

Such is the elegance of differentially periodic functions.
 

leehuan

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Re: MX2 2016 Integration Marathon

Very briefly, don't even need the substitution x=sin(theta) to verify your result. You can just let u=1-x^2.
 

porcupinetree

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Re: MX2 2016 Integration Marathon

If any 2016'ers are brave enough...

 

leehuan

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Re: MX2 2016 Integration Marathon

NVM found the mistake. Lol, sec^2 lee.
 
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leehuan

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Re: MX2 2016 Integration Marathon

Apart from L'Hopital's rule, is there any direct means of evaluating that limit? I did consider the limit but wasn't sure what to do within MX2
 

InteGrand

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Re: MX2 2016 Integration Marathon

Apart from L'Hopital's rule, is there any direct means of evaluating that limit? I did consider the limit but wasn't sure what to do within MX2
I doubt this integral would be asked in HSC MX2 these days.
 

leehuan

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Re: MX2 2016 Integration Marathon

I doubt this integral would be asked in HSC MX2 these days.
I suppose so. Paradoxica loves putting in extracurricular integrals here.
 
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