HSC 2012-14 MX2 Integration Marathon (archive) (5 Viewers)

Status
Not open for further replies.

U MAD BRO

Member
Joined
Jul 29, 2012
Messages
287
Gender
Undisclosed
HSC
N/A
Re: MX2 Integration Marathon

and this one =

The proofs for these integrals are extremely complicated... and obviously I used a resource "an introduction to the theory of numbers by hardy" and some other calculus book... will stop posting on this forum =(
 
Last edited:
Joined
Sep 20, 2010
Messages
2,225
Gender
Undisclosed
HSC
2012
Re: MX2 Integration Marathon

Lol. So much lol.

Next:

 
Last edited:

AAEldar

Premium Member
Joined
Apr 5, 2010
Messages
2,246
Gender
Male
HSC
2011
Re: MX2 Integration Marathon

Find this one WITHOUT using a trig substitution (and this includes hyperbolic functions, I don't want to see them). Spiral did this one a long time ago for me.

 

nightweaver066

Well-Known Member
Joined
Jul 7, 2010
Messages
1,585
Gender
Male
HSC
2012
Re: MX2 Integration Marathon

Find this one WITHOUT using a trig substitution (and this includes hyperbolic functions, I don't want to see them). Spiral did this one a long time ago for me.

so we can use other substitutions right











 
Last edited:

U MAD BRO

Member
Joined
Jul 29, 2012
Messages
287
Gender
Undisclosed
HSC
N/A
Re: MX2 Integration Marathon



MX2 level integral...

Final answer should be
 
Joined
Sep 20, 2010
Messages
2,225
Gender
Undisclosed
HSC
2012
Re: MX2 Integration Marathon

Well...1+x^4 is just testing an arduous and unpleasant partial fraction decomposition...not really getting to the core of integration.
 

U MAD BRO

Member
Joined
Jul 29, 2012
Messages
287
Gender
Undisclosed
HSC
N/A
Re: MX2 Integration Marathon

Well...1+x^4 is just testing an arduous and unpleasant partial fraction decomposition...not really getting to the core of integration.
You cannot do that with partial fractions.
 

Carrotsticks

Retired
Joined
Jun 29, 2009
Messages
9,494
Gender
Undisclosed
HSC
N/A
Re: MX2 Integration Marathon

I'll let one of the students do the honours. Quite a popular 'Harder Partial Fractions' problem, actually, along with 1/(x^3+1).
 
Joined
Sep 20, 2010
Messages
2,225
Gender
Undisclosed
HSC
2012
Re: MX2 Integration Marathon

COMPLETE THE SQUARE BITCHASS!



Now let things be...



Now it turns out that

Now you can factor out a 1/2 in the integrand.

After that you need to split the ax and b term (as well as cx and d) and they all become some sort of logs or inverse tans, depending on the sign of the fraction on the bottom. Then you can put the limits in, with inverse tan going to pi/2 as x goes to infty, and the logs will eventually cancel or simplify to give the required result.

What did you have in mind, UMAD? (To solve this integral)
 
Last edited:

U MAD BRO

Member
Joined
Jul 29, 2012
Messages
287
Gender
Undisclosed
HSC
N/A
Re: MX2 Integration Marathon

This is how it is done bitch :p




Much more concise.
 
Last edited:

U MAD BRO

Member
Joined
Jul 29, 2012
Messages
287
Gender
Undisclosed
HSC
N/A
Re: MX2 Integration Marathon

Carrot, if I use these techniques in the MX2 paper, do I get zero?
 

Carrotsticks

Retired
Joined
Jun 29, 2009
Messages
9,494
Gender
Undisclosed
HSC
N/A
Re: MX2 Integration Marathon

Hey hey c'mon keep it friendly and elementary.

And for the record UMAD, you didn't properly show the acquiring of the Laurent Expension and the substituting of the poles to acquire the Residue.

Carrot, if I use these techniques in the MX2 paper, do I get zero?
Yes.
 
Status
Not open for further replies.

Users Who Are Viewing This Thread (Users: 0, Guests: 5)

Top