HSC 2016 MX2 Integration Marathon (archive) (1 Viewer)

[Paradoxica]

Re: MX2 2016 Integration Marathon

I got this question off an integration bee btw

Yes, because you can't write your own questions.

 

[leehuan]

Re: MX2 2016 Integration Marathon

Yes, because you can't write your own questions.

I once did. And now I'm not motivated to.

 

[Drsoccerball]

Re: MX2 2016 Integration Marathon

Yes, because you can't write your own questions.

I never knew this was the "Only questions made by yourself Integration Marathon."

 

[Paradoxica]

Re: MX2 2016 Integration Marathon

I never knew this was the "Only questions made by yourself Integration Marathon."

It's not, but its more fun if it is.

 

[Drsoccerball]

Re: MX2 2016 Integration Marathon

It's not, but its more fun if it is.

If it isn't called, "Only questions made by yourself Integration Marathon," then stop making fun of people for using questions that are not theirs.

 

[Paradoxica]

Re: MX2 2016 Integration Marathon

never mocked them

but then again who knows what you see between the words

 

[leehuan]

Re: MX2 2016 Integration Marathon

never mocked them

but then again who knows what you see between the words

Bluntly putting it out that "you can't ..." sounds at the minimal like mocking.

The alternative was trying to insult me.

 

[abecina]

Re: MX2 2016 Integration Marathon

 

[leehuan]

Re: MX2 2016 Integration Marathon

._. Posted so many times now

 

[abecina]

Re: MX2 2016 Integration Marathon

._. Posted so many times now

Soz been out of the thread for a while - good to know its a fav

 

[leehuan]

Re: MX2 2016 Integration Marathon

Soz been out of the thread for a while - good to know its a fav

Yea dw about it lol, but at least 2 people have done it.


I'll sketch out the (slightly non-X2) method anyway.

1. Border-flip method allows two integrals to be summed up.
2. Use a log law just to put the thing that will generate the -pi/2 ln(2) aside
3. u-substitution combined with periodicity of sine
4. Riemann sums (or alternatively decompose using L'Hopitals)

 

[porcupinetree]

Re: MX2 2016 Integration Marathon

 

[DatAtarLyfe]

Re: MX2 2016 Integration Marathon

Soz but where did the sin2x go?

 

[InteGrand]

Re: MX2 2016 Integration Marathon

Soz but where did the sin2x go?

Mental substitution of u = 2x.

 

[DatAtarLyfe]

Re: MX2 2016 Integration Marathon

Mental substitution of u = 2x.

Oh ok, thanks

 

[leehuan]

Re: MX2 2016 Integration Marathon

This was a question I remember doing (at least a similar variant) last year. Not sure if it was ever posted again.

 

[Paradoxica]

Re: MX2 2016 Integration Marathon

This was a question I remember doing (at least a similar variant) last year. Not sure if it was ever posted again.

Recall the following identity:



Setting n=1008, gives us



Then the integral is the following sum:



This is the partial sum for the Leibniz formula for π, which has no elementary closed form.

 

[leehuan]

Re: MX2 2016 Integration Marathon

Probably a wrong boundary. Maybe it was meant to be pi, not pi/2

Edit: Hold the thought it still won't work. Ok fair enough

 

[Carrotsticks]

Re: MX2 2016 Integration Marathon

This is the partial sum for the Leibniz formula for π, which has no elementary closed form.

Yes it does. It will be some giant rational number.

We only really talk about 'closed forms' for infinite sums.

 

[Paradoxica]

Re: MX2 2016 Integration Marathon

Probably a wrong boundary. Maybe it was meant to be pi, not pi/2

Edit: Hold the thought it still won't work. Ok fair enough

You have forgotten an earlier conversation of your own which established the niceness of the generalised integral for only odd integer values.