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

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U MAD BRO

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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

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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

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Re: MX2 Integration Marathon

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

nightweaver066

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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

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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

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Re: MX2 Integration Marathon

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

 
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Re: MX2 Integration Marathon

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

seanieg89

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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

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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

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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.
 
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seanieg89

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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.
 
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