HSC 2015 MX2 Integration Marathon (archive) (5 Viewers)

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clbaker

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Re: MX2 2015 Integration Marathon

Alternatively, try the self-inverse substitution

Hint for others, exact value is a dead give away especially with zero at the lower limits.



Combine this with a clever substitution (trig).
 
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nightweaver066

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Re: MX2 2015 Integration Marathon

Err okay, were students expected to produce a non-elementary result? Kinda defeats the purpose of an integration bee.
The question was in a unique team event Integration Bee paper, specially designed for one team haha.

Of those questions, some probably required uni maths.
 

seanieg89

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Re: MX2 2015 Integration Marathon

Here is a primitive for , defined on the whole real line:

 

VBN2470

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Re: MX2 2015 Integration Marathon

NEW QUESTION:

 
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VBN2470

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Re: MX2 2015 Integration Marathon

Good job :). Answer could also be expressed as .
 

InteGrand

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Re: MX2 2015 Integration Marathon

NEW QUESTION:

We note that if , then . Hence the integrand is even, and our answer for positive t will be the same for negative t. Also note the inverse trig. identity

Now, let . Let . Then . Then changing the limits appropriately, we get









.

Edit: Wait, for negative t, the answer should be negative the answer for positive t, since we'd be integrating the area "the opposite way", right? In that case I think ?
 
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InteGrand

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Re: MX2 2015 Integration Marathon

Multiply the integrand by , then split the fraction into two components. This will get it into standard form, answer is .
Lol right method, except that the integral was an indefinite one. :)
 
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Re: MX2 2015 Integration Marathon

pls someone fix my eqn. im gonna cry with latex why is it invalid
 

VBN2470

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Re: MX2 2015 Integration Marathon

NEW QUESTION:

 
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