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

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

ok I will join. Can someone repost the ones that havnt been done please so i can see whats going on :D
Have a go at this mate :p (I procrastinate by doing uni maths ;) )





then consider the contour integral:



where the contour is the half-disc in the upper half plane, then just use the Residue Theorem.

Finish it :)
 

barbernator

Active Member
Joined
Sep 13, 2010
Messages
1,439
Gender
Male
HSC
2012
Re: MX2 Integration Marathon

<a href="http://www.codecogs.com/eqnedit.php?latex=i)~\int \frac{1}{x(x^{n-1}-1)}dx\\ \\ \frac{1}{n-1}\int \frac{n-1}{x(x^{n-1}-1)}dx\\ \\ (\frac{1}{n-1})(\frac{x^{n}}{n}-x)@plus;C\\ \\" target="_blank"><img src="http://latex.codecogs.com/gif.latex?i)~\int \frac{1}{x(x^{n-1}-1)}dx\\ \\ \frac{1}{n-1}\int \frac{n-1}{x(x^{n-1}-1)}dx\\ \\ (\frac{1}{n-1})(\frac{x^{n}}{n}-x)+C\\ \\" title="i)~\int \frac{1}{x(x^{n-1}-1)}dx\\ \\ \frac{1}{n-1}\int \frac{n-1}{x(x^{n-1}-1)}dx\\ \\ (\frac{1}{n-1})(\frac{x^{n}}{n}-x)+C\\ \\" /></a>
 

john-doe

Member
Joined
Jul 29, 2012
Messages
179
Gender
Male
HSC
2012
Re: MX2 Integration Marathon

sorry to ask without answering but can someone show me how to integrate dx/(sinx-cosx) thanks!
 

nightweaver066

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

sorry to ask without answering but can someone show me how to integrate dx/(sinx-cosx) thanks!
should be making your own thread.

use the change sinx - cosx in to the form of Rsin(x - alpha), or you can use t substitution
 

seanieg89

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

sorry to ask without answering but can someone show me how to integrate dx/(sinx-cosx) thanks!
Use the auxillary angle method to write the denominator as Rcos(x+alpha). Sec should be a function you know how to integrate.
 

seanieg89

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

Here is a question of a different flavour, but easier than most in this thread so far:

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

Aren't recurrence formulas for 2 parameters (n and m) not in the syllabus? (just wondering)
 

seanieg89

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

Aren't recurrence formulas for 2 parameters (n and m) not in the syllabus? (just wondering)
Perhaps, but then again I am not asking for an explicit recurrence formula :).

You should be able to integrate many integrals of this form without recursive methods.
 

graphs

New Member
Joined
Mar 19, 2012
Messages
1
Gender
Female
HSC
2012
Re: MX2 Integration Marathon

i dont know what this is called, but can you just swap the order of the numbers that are on the integral sign when there's a minus number and you want it gone?
 

U MAD BRO

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

i dont know what this is called, but can you just swap the order of the numbers that are on the integral sign when there's a minus number and you want it gone?
Yes, you can.
 
Last edited:

seanieg89

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

can you even do your own integrals?
If by do, you mean look up the answer using whichever resource he got those integrals from in the first place then yes he can.
 
Status
Not open for further replies.

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

Top