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I=\int sin5xcos3x dx \\ Let \ u = sin5x , \ dv=cos3x dx \\ \therefore du/dx = 5cos5x , \ v= \frac{1}{3}sin3x \\ \therefore I=\frac{1}{3}sin5xsin3x - \int\frac{5}{3}sin3xcos5x dx \\ Let \ u=sin3x , \ dv=cos5xdx \\ du/dx=3cos3x , \ v=\frac{1}{5}sin5x \\ \therefore I=sin5xsin3x -...

Um, why have you quoted hyperbolic functions? :O

No. 1. \omega =\frac{2\pi}{T} is not a definition. 2. It only applies to uniform circular motion.

Question: A point P is moving in a circular path around a centre O. Define the angular velocity of P with respect to O at time t. Derive expressions for the tangential and normal components of the acceleration of P at time t.

I=\int_0^4\frac{x}{\sqrt{x+4}}dx=\int_0^4\frac{x+4-4}{\sqrt{x+4}}dx=\int_0^4\sqrt{x+4}-4(x+4)^{-1/2}dx etc :P

Don't be lazy and post the question. Don't be such an insult to those willing to help you with the question. And why exactly do you need help with this when you finished your HSC in 2007?

Pfft. Surgeons don't get paid much (in comparison). Become an Kerry Packer :D

Nope. But it's not hard. Probs wouldn't hurt learning it.

It's not working too well LOL :P

I'm not too sure since I've never really used this method. But I was under the impression that you need 6 cases. (ie. all possible combinations of negative and positive cases) Taking cases, like you've done. But why would you? It's like me saying that I'll always use the first principle...

That's a very annoying way of doing this (especially because you now have 3 factored terms). So you would need to take 6 cases, not just the 4 that you've mentioned I believe.

This is true. Except for nuclear fission related calculations in the Quantum to Ducks options module. I'm not too sure about this. Because quite a few times (eg. titrations and mole calculations) you are dealing with small quantities... I don't think this is necessary for the HSC.

Don't talk to yourself --> It's a bad habit.

I never said that I was ;) (Interestingly enough though, I can still do simple inequalities :D)

That's just novice. *he's

People who are arrogant don't say "Look here! I'm arrogant". Likewise, need I say more?

Yeah but he doesn't even know how to solve simple inequalities... I'd be suprised if he knew the difference between his elbow and backside.

Gold. :rofl:

Dude, it's just like me saying that I forgot how to do mental arithmetic for simple calculations just because I haven't done them in a while (ie. because I've been using a calculator in the HSC)... Plus this stuff you would've needed for Q1 or 2 of the Ext 1 paper... So it's not that long ago...

This person speaks the truth.