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

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Paradoxica

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Re: MX2 2016 Integration Marathon

Whats wrong with my working out though ?
Because in my question, k must be an integer, because the sub-scripted k means you must nest the logarithm "k" times. What does it mean to iterate a function 1.5 times? Nonsense, that's what. (This comment assumes you do not know what a functional square root is)

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leehuan

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Re: MX2 2016 Integration Marathon

Because in my question, k must be an integer, because the sub-scripted k means you must nest the logarithm "k" times. What does it mean to iterate a function 1.5 times? Nonsense, that's what. (This comment assumes you do not know what a functional square root is)





Typical question.

First find the integral of the arcsine using, IBP. Then do the resulting integral, using, IBP.

Also, nice revenging on Drsoccerball LOL...
 

Drsoccerball

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Re: MX2 2016 Integration Marathon

Typical question.

First find the integral of the arcsine using, IBP. Then do the resulting integral, using, IBP.

Also, nice revenging on Drsoccerball LOL...
Dw if there's a long one I can do Ill get him back.
 

Drsoccerball

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Re: MX2 2016 Integration Marathon

how can you assume that xlnx → 0 as x→ 0? You need to properly justify this using mx2 tools
My bad I was so obsessed with the Paradoxica thing I forgot about that. Use rectangles.
 

InteGrand

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Re: MX2 2016 Integration Marathon

Yes, the answer is clearly positive as the integrand is positive throughout the domain of integration. I can't really read (or be bothered to decipher) Drsoccerball's solution though since there are too many "Paradoxica" and "Drsoccerball" references in the working :p...but I assume he made an algebraic mistake somewhere.
 

leehuan

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Re: MX2 2016 Integration Marathon





A clever 2016er can do this.
 

InteGrand

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Re: MX2 2016 Integration Marathon





A clever 2016er can do this.
This is just a standard log solution. We can simplify the sum of k's using an A.P. sum formula. Did you possibly mean product instead of sum on the denominator (makes it more interesting)?
 
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