Search results

Re: HSC 2013 4U Marathon haha nice, I didn't know this was the original method. I heard that his original method wasn't very rigorous so now I know why. Which one is your favorite method to compute \zeta (2)?

Re: HSC 2013 4U Marathon I think it should be 0 < \theta < 2\pi Can I do this using Fourier or Taylor series since they use elementary functions and some integration?

Re: HSC 2013 4U Marathon I tried to sub the roots of cosx into part (ii) then differentiate but I can't get the answer yet :( I know that I have to follow the steps blah blah blah but it can be proved much more rigorously using \zeta (2) There are many proofs of \zeta (2) here...

Re: MX2 Integration Marathon $Let$ I_{n} = \int_{0}^{k}(k^{2}-x^{2})^{n}dx $Let$ u=(k^{2}-x^{2})^{n} \therefore du=-2nx(k^{2}-x^{2})^{n-1} dv=dx, v=x \therefore I_{n} = -2n\int_{0}^{k}(k^{2}-x^{2}-k^{2})(k^{2}-x^{2})^{n-1}dx...

Re: MX2 Integration Marathon Will do that from now on, thanks.

Re: MX2 Integration Marathon \int \sin^{3}x\sin(203x)dx

Re: MX2 Integration Marathon I like how you used m and then set it to one, I don't see anything wrong with the method but I did it differently. Will post my solution later.

Re: HSC 2013 4U Marathon This is a simple Fourier series called sawtooth function. I still can't find a way to do it using MX2 methods. Can you give a hint?

HSC physics is shit*

Re: MX2 Integration Marathon Yes.

I do all three sciences, I think HSC bio is more difficult than chem. There is just too much content in bio and a lot of memorisation is required making it very time consuming.

HSC sciences are a joke. The only good HSC subjects are maths extensions but I wish it covered matrices and linear algebra as these are very important in university maths. There is a lot of focus on calculus, which is great, but linear algebra is important too.

Re: HSC 2013 4U Marathon Good question but 'thinking up of' a function etc. is very tricky and I think this question would be more 4U level if you said consider \sum_{r=0}^{n} (-1)^{r} \binom{n}{r} x^{m+r} hence prove etc. $Consider the sum:$ \sum_{r=0}^{n} (-1)^{r} \binom{n}{r} x^{m+r} =...

Re: MX2 Integration Marathon Nice!

Re: HSC 2013 4U Marathon The RHS is the beta function https://en.wikipedia.org/wiki/Beta_function, I'm I allowed to use it to prove this?

Re: HSC 2013 4U Marathon Do you do this questions using the conjugate root theorem?

Re: MX2 Integration Marathon \int \frac{dx}{x^{n}(x-a)}

Re: MX2 Integration Marathon A way to come up with really complicated integrals that can be done using elementary functions: make up a complicated function and differentiate it :D

The HSC is a competition, that should be more than enough to motivate you.

Re: MX2 Integration Marathon $Evaluate the following integral:$ I(r)=\int_0^\pi\ln(1-2r\cos x+r^2)dx $where$ \lvert r\rvert\neq1