ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: kj_ on September 25, 2008, 12:09:31 am

Title: Integration
Post by: kj_ on September 25, 2008, 12:09:31 am: This -might- be over the level of specialist, I'm not too sure, but if anyone would like to have a go at:

$\int{\frac{x^2}{9+x^6}}dx$

puzzling me out :o
Title: Re: Integration
Post by: Collin Li on September 25, 2008, 12:11:35 am: It's not on the Specialist course (AFAIK, non-linear substitutions are not allowed unless they are simple trigonometric substitutions - or they tell you the substitution), but using the substitution $u = x^3$ should work out nicely.
Title: Re: Integration
Post by: shinny on September 25, 2008, 12:13:56 am: As coblin said, let u=x^3, du/dx=3x^2, and after just two steps or so, you'll end up with
$\frac{1}{9}Tan^{-1}(\frac{x^{3}}{3})$
Title: Re: Integration
Post by: kj_ on September 25, 2008, 12:14:39 am: ah, works out very cleanly - thanks!

and wow, quick reply coblin :)