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HSC 2018-2019 MX2 Integration Marathon (1 Viewer)

Paradoxica

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Re: HSC 2018 MX2 Integration Marathon

but in the hsc such a question would not be likely to appear, all that work just for a simple integral....
 

mrbunton

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Re: HSC 2018 MX2 Integration Marathon

only requires u substitution.
 
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fan96

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Re: HSC 2018 MX2 Integration Marathon





Justifying this substitution:

has a solution for only when and .

The domain of the integrand is and .

does not exist only when . But since this range is undefined in the integrand to begin with, the substitution is valid.

So,



Substituting, we get



Not sure if that second last step was valid though.

(edit: oops forgot to sub back in)

And so



and by considering the appropriate right angled triangle, . Since that's always positive, the sign function on the left can be eliminated.

So we have

 
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jathu123

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Re: HSC 2018 MX2 Integration Marathon

an easier way is to just use the substitution u = sqrt(x)
the integrand will be 2/sqrt(u^2+1), which is trivial to integrate (those usual log ones)
 

mrbunton

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Re: HSC 2018 MX2 Integration Marathon

correct but the two tan signs are generally said to cancel each other out; although i understand it can vary from +-1. that being said if u look at example at the integral tanx/|tanx| it is a horizontal line being split up into positive and negative in pi/2 segments at a time and hence u should not be allowed to take it out theoretically (although area stays the same; definite integral get affected from my understanding)but discontinuous graphs in integration are probably beyond the scope of even ext2(when dealing with indefinite integrals btw; or i havent been taught it yet). Its easier just to cancel the tan out imo at this level.

im not completely sure but in the solution i got had the tan cancelled out
 
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Paradoxica

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Re: HSC 2018 MX2 Integration Marathon

is anyone else seeing a bunch of extra addition symbols lodged between every character or is that just me
 

Paradoxica

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HSC 2018 MX2 Integration Marathon

an easier way is to just use the substitution u = sqrt(x)
the integrand will be 2/sqrt(u^2+1), which is trivial to integrate (those usual log ones)
may as well just jump ahead and multiply by
 

supR

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Re: HSC 2018 MX2 Integration Marathon

is anyone else seeing a bunch of extra addition symbols lodged between every character or is that just me
Yeah I'm seeing that and it's really confusing


Sent from my iPhone using Tapatalk
 

HeroWise

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Re: HSC 2018 MX2 Integration Marathon

is it 13/15 pi u^2 ??
 

fan96

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Re: HSC 2018 MX2 Integration Marathon

Can someone give me a hint for this question?

 
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