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Re: HSC 2018 MX2 Integration Marathon Hint: expand and substitute

Re: HSC 2017 MX2 Marathon I think LaTeX broke

Enjoy the integral... ε= *cackles maniacally*

Then what is god? Nothing is above existence. anything that can exist can be referred to as "it" if the properties of "it" are unknown. This also applies to metaphysical concepts.

I'm getting O(x⁻¹) Differentiating under the integral sign yields: f'(x) = \sin{x} \left(\frac{1}{x+2\pi} - \frac{1}{x}\right) = \sin{x} \left(-\frac{2\pi}{x^2} + \frac{4\pi^2}{x^3} + \mathcal{O}\left(x^{-4} \right) \right) Ignore sin x and integrate both sides to obtain an asymptotic...

hence why we are shit with our technology... everything is probability these days...

Re: HSC 4U Integration Marathon 2017 ...ew

Re: HSC 4U Integration Marathon 2017 Eliminate irrational functions using whatever you have at your disposal. The only three ways of doing so are: Classical Trigonometric Substitution (High School level) Hyperbolic Trigonometric Substitution (University level) Euler Substitution...

Re: HSC 2017 MX2 Marathon ADVANCED A square pyramid has height exactly half it's base side length, a. Find the volume of the pyramid.

Re: HSC 2017 MX2 Integration Marathon If b>a>0 evaluate: \int_{\tfrac{1}{b}}^{\tfrac{1}{a}} \dfrac{\tan^{-1}{ax} - \cot^{-1}{bx}}{x} \, \text{d}x

Nice stack exchange steal.

\int_0^\frac{\pi}{2} \frac{\tan^{-1}{(a\cos^2{x})}}{\cos^2{x}} \, \text{d}x

Why have the latest seasons been so political... JFC

$\noindent $ y = \frac{2-\sin{\theta}}{2\tan{\theta}} = \cot{\theta} - \frac{\cos{\theta}}{2} Stop here. cot(θ) is unbounded and cos(θ) is bounded as θ → 0, so the maximum value does not exist.

This is purely an observational thread, although you may choose to answer them anyway. Post the most evil integrals you -have ever/happen to- come across in your mathematical endeavours. And optionally, make a few observational comments on the integral, and any attempted evaluations of it...

Re: Why is english compulsory if if has no relevance to the real world (read more bel Yeah, both subjects at their core boil down to the same few flaws that have plagued the entire education system for decades.

Re: Why is english compulsory if if has no relevance to the real world (read more bel Probably. I mean at the end of the day Mathematics is a language like any other except the "rules" are just some axioms. The rest of Mathematics trivially follows from that... It has it's own dialects...

Re: Why is english compulsory if if has no relevance to the real world (read more bel Let's change this slightly... And that is exactly what it's like for mathematics. #centuryoldeducationsystem

Re: Why is english compulsory if if has no relevance to the real world (read more bel ->chinese stem genius this triggers me In all seriousness I have semi-decent people skills but like... The wall that is academia is unyielding to my problems. :') #Sub80ATARproblems