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Re: 2012 HSC MX2 Marathon One last question then sleep for me. $Prove via mathematical induction $ (cosx + isinx)^n = cosnx + isinnx Goodnight.

Re: 2012 HSC MX2 Marathon Haha ok, I'll let you go to the toilet :D Plus I'm out of standard integrals to post lol.

Re: 2012 HSC MX2 Marathon $Show that $\int \frac{1}{\sqrt{a^2 + x^2}}dx = ln|x +\sqrt{a^2 + x^2}| + c Then \int \frac{1}{\sqrt{x^2 - a^2}}dx = ln|x +\sqrt{x^2 - a^2}| + c

Re: 2012 HSC MX2 Marathon That's it. Next one. $Show that $\int \frac{1}{\sqrt{a^2 - x^2}}dx = sin^{-1}\frac{x}{a} + c

Re: 2012 HSC MX2 Marathon That works, can you do it the other way though?

Haha, sometimes the simplest things can end up being the hardest.

Re: 2012 HSC MX2 Marathon Haha that makes sense. 4U integration is much better :P Here's another one: $Prove $ \int \frac{1}{1+x^2}dx = tan^{-1}x + c Not much harder then 3U, except you have to figure out the substitution :D

Re: 2012 HSC MX2 Marathon It's all right until the last bit \int^6_3 2f(x) - 3dx = 2\int^6_3f(x)dx - \int^6_3 3dx = 60 - [3x]^6_3 = 60 - (18 - 9) =51 Have you done integration yet?

It's ok, asking questions is good! $The chain rule is used for when there is a function within a function $f(g(x)) $When we differentiate a function like this, we differentiate the first function, and then times it by the derivative of the second function $ \\ \frac{d}{dx}f(g(x)) =...

Re: 2012 HSC MX2 Marathon Guess it's time for a question, don't want this thread to die! $If $\int^6_0f(x)dx=42 $and $\int^3_0f(x)dx=12, $Find $\int^6_32f(x)-3dx

Do you remember the chain rule?

Are you sure you can't delete them? One of the screens should let you remove/swap your classes.

If you're good at it, and enjoy it then it'll be beneficial.

Re: 2012 HSC MX2 Marathon =( It's ok, I'm doing as much math as possible :D

Please continue..

Re: UNSW Roll Call 2012 Didn't you save it when made the password? :(

Advanced Science at UNSW :)

No one sane. It's hard enough using latex on here.

I prefer handwriting. Means I can draw easily, and it's a lot better with maths :D

America is a sad country when it comes to things like this...