VCE Specialist 3/4 Question Thread!

[paulsterio]

yep, confirmed it, they are both right, both give cos(x) / (sin(x))^3 after differentiation

[b^3]

Remember that 1/sin^2(x) is csc^2(x)
Now also note that 1+cot^2(x)=csc^2(x)

Now what you have are translations of each other along the y axis, as the +C is not the same in both cases,
i.e. -1/2cot^2(x)=-1/2*(csc^2(x)-1)+C1
=-1/(2sin^2(x))+1/2+C1
=-1/(2sin^2*x) +C2 where C2=1/2+C1

I.e. it is just a translation on the y-axis, as you get two different C's but they are both correct.

Hope that helps and I hope there aren't any mistakes in there (it is likely, I'm pretty tired right now)

[xZero]

firstly the 2nd answer should be -1/2*csc^2(x), anyways heres a hint, 1+cot^2(x)=csc^2(x)

[Special At Specialist]

I get it now. They are the same graph (and same gradient) but a different translation.
Thank you

[b^3]

Code: [Select]

\underset{\sim}{j}

e.g.

[Special At Specialist]

Do we need to know integration by parts?
Should I learn it just incase?

[abd123]

Do we need to know integration by parts?
Should I learn it just incase?

I heard integration by parts is useful for complicated derivatives via 'product rule' right? I think it would a good idea to learn it.
Don't know if VCAA examiners would accept that process of integration though .

[pi]

Do we need to know integration by parts?
Should I learn it just incase?

You can learn it to check answers, but can't use it in the exams

[Special At Specialist]

I heard integration by parts is useful for complicated derivatives via 'product rule' right? I think it would a good idea to learn it.
Don't know if VCAA examiners would accept that process of integration though .

That's unlucky I've never really found derivatives complicated, it's integration that sometimes messes with my brain. Speaking of which:
Show that for a>0 =

[pi]

Can't you let and work from there? Things should cancel out I think.

I'm really out of it lol

[TrueTears]

Do we need to know integration by parts?
Should I learn it just incase?

a quick tutorial if u ceebs wiki-ing it Re: Specialist Summer Holidays Question Thread!

[Special At Specialist]

Do we need to know integration by parts?
Should I learn it just incase?

a quick tutorial if u ceebs wiki-ing it Re: Specialist Summer Holidays Question Thread!

That was very helpful and unlike Wikipedia, I can actually understand it Thank you!

I pm'd the last problem to Thushan. Hopefully he can solve it.

[pi]

Yeah, you know how to do that

(do it the long way, and not multiply by the identity btw)

[samad]

Hey, that question involves partial fractions:
express the integral:

Now:

Using standard partial fractions techniques
now the integral is:


as required
pi's appraoch very valid as well but not on course

Moderator action: removed real name, sorry for the inconvenience

[pi]

lol, I was so off