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HSC 2016 MX2 Integration Marathon (archive) (8 Viewers)

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math man

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Re: MX2 2016 Integration Marathon

you still have to do the expansion of the radical and the factorisation, which, for most students is +3 lines
Well it took me 1 sec so I suppose that's why I'm saying my way is quicker
 

leehuan

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Re: MX2 2016 Integration Marathon

Most of the time I don't like 1-x^2 at all. It's only better this time because it's under a square root. If something came down to be trivial like 1/√(1-x^2) that I won't complain about obviously.

But the expansion process, whilst I figured wasn't something messy (by that I mean easily factored), isn't exactly something convenient either.
 

math man

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Re: MX2 2016 Integration Marathon

You might be accustomed to speedy computations, but my brain prefers using magic.
Yeh I'm literally a speed demon, doubt there are many that can match my speed, in 2nd year math2961 I did the final exam 3 times in the 2 hour period lol, but I'm also excellent with magic
 

Paradoxica

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Re: MX2 2016 Integration Marathon

Yeh I'm literally a speed demon, doubt there are many that can match my speed, in 2nd year math2961 I did the final exam 3 times in the 2 hour period lol, but I'm also excellent with magic
Which is why you should not be holding us to your own standard.

Don't have me calling you out on this again.
 

leehuan

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Re: MX2 2016 Integration Marathon

That sad moment when you can't use a convenient substitution
 

Paradoxica

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Re: MX2 2016 Integration Marathon

That sad moment when you can't use a convenient substitution
Technically you can.

You have to split the integrand into two pieces, one can be substituted, the other one is a bit trickier.

Hint:

4 + 4x4 ≡ 2 + 6x4 + 2(1-x4)
 
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math man

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Re: MX2 2016 Integration Marathon

Technically you can.

You have to split the integrand into two pieces, one can be substituted, the other one is a bit trickier.

Hint:

4 + 4x4 ≡ 2 + 6x4 + 2(1-x4)
Why not split it like (x+2)((x^4-1)+2) ?
 

math man

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Re: MX2 2016 Integration Marathon

Well I used some nice magic with my method, I'll try yours then.
 
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