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Yo guys what's the method of finding kinetic energy for last q using binding energies

I felt like for many of the section 2 questions, they were designed for you to argue against the question or at least to a non-significant extent. Personally I did Dobson, and i argued that it was true to a medium extent (did for the question for Young girl, cock crow and then went against for...

so just marking q11 of the 4u papers I seem to notice a couple of common trends: -for the first integral many methods and manipulations were used with most of them being fruitless (and someone even told us to research an identity smh) -for the volumes question, many people got the correct bounds...

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Show that \int_0^{\tfrac{\sqrt{6}-\sqrt{2}-1}{\sqrt{6}-\sqrt{2}+1}} \dfrac{\ln x}{(x-1)\sqrt{x^2-2(15+8\sqrt{3})x+1}}dx=\dfrac{2}{3}(2-\sqrt{3})G where G is Catalan's constant.

Re: HSC 2018 MX2 Marathon Continuing on, prove that the area of the ellipse defined by \frac{(a x + b y)^2}{p^2} + \frac{(cx + dy)^2}{q^2} = 1 has area \frac{\pi p q}{|ad - bc|}

Re: Extracurricular Integration Marathon Can you please show working out? I can't really learn from this and what is this "slight manipulation" that you have stated.

Re: HSC 2018 MX2 Integration Marathon Yup. FYI the mistranscribed integral is equivalent to 1/root(2) integral of root(tanx) which has been calculated to exhaustion.

Re: HSC 2018 MX2 Integration Marathon Further hint: take something out of the root and simplify, then substitute

Well done! This is basically the solution I have as well.

Can a cube be inscribed in a cone so that 7 vertices of the cube lie on the surface of the cone?

These questions are very easy compared to standard HSC-type examination questions. Most of these are doable by inspection and are thus left as exercises to the reader

Re: HSC 2017 MX2 Marathon ADVANCED ewwww formula pleb jkjk

Re: HSC 2017 MX2 Marathon ADVANCED It's just \frac { { a }^{ 3 } }{ 6 } . Consider a cube with side length a. If you cut along its diagonals u get 6 identical pyramids with height half the base.

Re: HSC 2017 MX2 Integration Marathon Trivial by inspection $\noindent$ I=\int_{\tfrac{1}{b}}^{\tfrac{1}{a}} \dfrac{\tan^{-1}{ax} - \cot^{-1}{bx}}{x} \, \text{d}x \\\\ $Let $ x=\dfrac{1}{y} \\\\ \text{d}x = \dfrac{-\text{d}y}{y^2} \\\\ I=\int _b^a...

$\noindent$\int { \frac { \tan ^{ -1 }{ x } }{ x } } { (\frac { { x }^{ 3 } }{ 1+{ x }^{ 6 } } ) }^{ 8 }dx \\ $This one is absolutely terrible with its closed form primitive being utterly disgusting.$ \\ $However$ \\ \int _{ 0 }^{ \infty }{ \frac { \tan ^{ -1 }{ x } }{ x } } { (\frac { { x...

Re: Extracurricular Integration Marathon \begin{align*}a)\int _{ 0 }^{ 1 }{ ln(1-x){ \{ \ln { { (x)\} } } }^{ n-1 }\frac { dx }{ x } }\\b)\int _{ 0 }^{ 1 }{ ln(1+x){ \{ \ln { { (x)\} } } }^{ n-1 }\frac { dx }{ x } }\end{align*}

Re: HSC 2017 MX2 Integration Marathon a) \quad Let\quad I=\int { \frac { dx }{ x\sqrt { { x }^{ 10 }\pm { x }^{ 5 }+1 } } } \\ Let\quad u={ x }^{ 5 }\\ du=5{ x }^{ 4 }dx\\ I=\frac { 1 }{ 5 } \int { \frac { du }{ u\sqrt { u^{ 2 }\pm u-1 } } } \\ \quad =\frac { 1 }{ 5 } \int { \frac { du }{...

Re: Why is english compulsory if if has no relevance to the real world (read more bel You deserve some rep for this statement

Re: First Year Uni Calculus Marathon Let\quad \beta \quad be\quad a\quad real\quad positive\quad real\quad numberLet\quad { a }_{ n }\quad be\quad a\quad sequence\quad of\quad positive\quad real\quad numbers\quad such\quad that:\\ \lim _{ n\xrightarrow { } \infty }{ \frac { 1 }{ { n }^{...