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

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Paradoxica

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Re: MX2 2016 Integration Marathon

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

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


This has no nice form I am aware of.

Actually. Ignore that. That's way out of HSC.

Here's something which looks more reasonable.

 

Paradoxica

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Re: MX2 2016 Integration Marathon

I think I love the 2nd one lol, looks so ugly but is really easy
I do my best to avoid tedious integrals.

However, tedious integrals are the very first integrals I used to teach myself integration. Without it, I don't think I could integrate by inspection as quickly or as easily as I can today.
 

leehuan

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Re: MX2 2016 Integration Marathon

Out of curiosity is the first one supposed to be another symmetric substitution lol
 

math man

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Re: MX2 2016 Integration Marathon

For the first one is there another way to do it besides P.Fs otherwise ceebs
 

leehuan

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Re: MX2 2016 Integration Marathon



Then I got lazy.

But apparently the resulting integral when put into wolfram is neat.
 

leehuan

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Re: MX2 2016 Integration Marathon

Hint: Double Angle
Lol ok I see it now yep.

But yeah I'll let someone else finish it. I should be doing this assignment but I'm procrastinating
 

math man

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Re: MX2 2016 Integration Marathon

Wow you used wolfram to factorise, they fully factored it. You can't rely on programs to do the math for you cause they don't know all the little tricks
You get 4x^2(1-x^2), take the 4x^2 out the square root
 

leehuan

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Re: MX2 2016 Integration Marathon

Wow you used wolfram to factorise, they fully factored it. You can't rely on programs to do the math for you cause they don't know all the little tricks
You get 4x^2(1-x^2), take the 4x^2 out the square root
And you're left with (1-x^2) which is still untidy.
 

math man

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Re: MX2 2016 Integration Marathon

The x cancels with numerator and you're left integrating x/sqr(1-x^2) which is a joke
 

Paradoxica

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Re: MX2 2016 Integration Marathon

The x cancels with numerator and you're left integrating x/sqr(1-x^2) which is a joke
Still a heck of a lot longer than reversing the double angle expansion of the argument and then integrating by inspection.
 

math man

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Re: MX2 2016 Integration Marathon

And you're left with (1-x^2) which is still untidy.
Also having a 1-x^2 is not untidy as having that on the denominator you should be like Yess!! Cause there are so many ways to integrate that which are all easy
 

math man

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Re: MX2 2016 Integration Marathon

Still a heck of a lot longer than reversing the double angle expansion of the argument and then integrating by inspection.
It takes 2 lines, I don't know if that's a lot longer
 
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