MedVision ad

HSC 2012-14 MX2 Integration Marathon (archive) (1 Viewer)

Status
Not open for further replies.

Sy123

This too shall pass
Joined
Nov 6, 2011
Messages
3,730
Gender
Male
HSC
2013
Re: MX2 Integration Marathon

not sure if i got this right, but i got



i substituted u = sinx then did partial fractions with
That looks like a different form to what I had but correct, well done, all I did was:



Which is easily integratable
 

aDimitri

i'm the cook
Joined
Aug 22, 2013
Messages
505
Location
Blue Mountains
Gender
Male
HSC
2014
Re: MX2 Integration Marathon

Ah right, that makes a lot of sense. I got it to that stage but I always forget that partial fractions is an option with trig :p
 

seanieg89

Well-Known Member
Joined
Aug 8, 2006
Messages
2,662
Gender
Male
HSC
2007
Re: MX2 Integration Marathon

A function defined on the reals is said to be T-periodic if f(x+T)=f(x) for all x. (T is a positive real number).

Show that the integral of a continuous T-periodic function over ANY interval of length T is the same.
 

aDimitri

i'm the cook
Joined
Aug 22, 2013
Messages
505
Location
Blue Mountains
Gender
Male
HSC
2014
Re: MX2 Integration Marathon

ok so what we are trying to prove is that

i'm not sure how valid my method is for this but

 

seanieg89

Well-Known Member
Joined
Aug 8, 2006
Messages
2,662
Gender
Male
HSC
2007
Re: MX2 Integration Marathon

ok so what we are trying to prove is that

i'm not sure how valid my method is for this but

Good work, but notice that your working depends on k being an integer. So you have only proven the claim for intervals like [7T,8T] or [-3T,-2T], but not for intervals like [1.5T,2.5T].

(The notation [a,b] refers to the closed interval a =< x =< b)
 

aDimitri

i'm the cook
Joined
Aug 22, 2013
Messages
505
Location
Blue Mountains
Gender
Male
HSC
2014
Re: MX2 Integration Marathon

Yeah I realised that after but am yet to solve this problem, will have a crack at it tomorrow morning at school :)

EDIT:
ok i think i've got it now!

 
Last edited:

Davo_01

Active Member
Joined
Apr 8, 2014
Messages
116
Gender
Male
HSC
N/A
Re: MX2 Integration Marathon

Yeah if you intuitively can see it's xln(lnx) then you're lucky, but what IBP did you use on ln(lnx)? That seems a lot faster than my method.




 
Last edited:

Fade1233

Active Member
Joined
Jun 1, 2014
Messages
345
Gender
Undisclosed
HSC
N/A
Re: MX2 Integration Marathon

Good question.

Can't use latex sorry.
 
Last edited:
Status
Not open for further replies.

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top