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Re: MX2 Integration Marathon 1. Let u^2 = x 2. IBP I = 2\left ( \frac{u^2}{2}tan^{-1}u - \frac{1}{2}\int \frac{u^2du}{1+u^2} \right ) +C \\ \\ I = 2 \left ( \frac{u^2}{2}tan^{-1}u - \frac{1}{2} \left ( u - tan^{-1}u \right )\right ) +C \\ \\ I = x tan^{-1} {\sqrt{x}} + tan^{-1}{\sqrt{x}} -...

P(x) = (x-2)^2 (px+q) P(1) = 6 --> P(1) = p + q = 6 P(3) = 8 --> P(3) = 3p + q = 8 Simultaneously solve for p and q P(x) = (x-2)^2 (x + 5) Might expand.. no other way i can think of is this a 4u question?

Re: MX2 Integration Marathon I = \int_0^{\frac{\pi}{2}}\sqrt{1+sin2x}dx \\ \\ $By skipping many steps of trig identities\\ \therefore I = $\int_0^{\frac{\pi}{2}}|sinx + cosx|dx \\ \\ \therefore I = \sqrt{2}\int_0^{\frac{\pi}{2}} |sin(x + \frac{\pi}{4})|dx \\ \\ 0\leq x\leq \frac{\pi}{2}\\...

Re: HSC 2013 4U Marathon "Fired with a velocity of theta to the horizontal" anything wrong with this? or ntohing wrong?

Re: MX2 Integration Marathon let t = tan(x/2) *Skip working out* I = \int_0^1 \frac{dt}{(t^2+1)|t+1|} \\ \\ $From limits (what do I call it?), \\ 0 \leq t \leq 1 \\ \therefore t+1\geq 0 \\ \\ \therefore I = $\int_0^1\frac{dt}{(t^2 + 1)(t+1)} \\ \\ $ Apply partial fractions and u get...

Re: HSC 2013 3U Marathon Thread Sorry i wasnt specific Pretend, I = Z Split 4 times, I = |A|+ |B| + |C| + |D| I = A + B + |- C - D| (i was talking about these absolute values) i can eliminate each absolute value from each (sinx) because of ASTC For, 0 ≤x≤ pi/2, sinx >0 (A) For, pi/2 ≤...

Re: HSC 2013 3U Marathon Thread $Let I = $\int_0^{2\pi} \sqrt{1-\cos^2 x} \ dx \\ I = \int_0^{2\pi}|sinx|dx \\ \\I = \int_0^{\frac{\pi}{2}}|sinx|dx + \int_{\frac{\pi}{2}}^{\pi}|sinx|dx + \int_{\pi}^{\frac{3\pi}{2}} |sinx|dx + \int_{\frac{3\pi}{2}}^{2\pi}|sinx|dx \\ A.T.S.C ($A turtle seeking...

You can :) \frac{12t}{t^2 +4}L/min $means: \\ \\ $\frac{dV}{dt} = \frac{12t}{t^2 + 4} \\ dV = \frac{12t}{t^2 +4}dt \\ \therefore \int dV = 12\int \frac{t}{t^2 +4}dt \\ \int dV = \frac{12}{2}\int \frac{2t}{t^2 +4}dt \\ \therefore V = 6ln(t^2 +4)+ C \\ \\$ $At $ t = 0, v = 0, \therefore C =...

aight thanks!

when can i transfer?

1. Whats the difference in doing BCom/BSc at USyd and UNSW? 2. Say i pick chemistry or physics for science and i fail it or lost my interests on it, what will happen? Thanks to every human who answers this! :D

re: HSC Physics Marathon Archive Electron–positron annihilation!

{\dot{x}} x -dot {\ddot{x}} x-double dot

u arent dumb, u just need more practice to see the beauty of maths. Having a gloomy mentality is not good, it makes u worse as i've experienced it last year remember to use all the information given in the question and NEVER BACK DOWN!

Define microeconomic policies and u'll know what to do next

L: m_L \perp m_{AB}\\ \\ \therefore m_L.m_{AB} = -1 \\\\ \therefore m_L = \frac{-1}{m_{AB}} \\\\ \therefore m_L = \frac{-1}{\frac{4-(-2)}{2-5}} ($using m = $\frac{y_2 - y_1}{x_2 - x_1})\\ \\ \therefore m_L = \frac{1}{2} Line L passes through C (1,-1) Using one-point gradient formula or w/e u...

i told u what do...

-dont be afraid -try to concetrate a lot while ur studying, some teachers say 'ur performance in ur test reflects how much u study and how u study'. So if u concentrate and do practice questions just like if they were in the test (TO THE BEST OF UR ABILITY), u'll do fine -logic is ur best friend...

x^2 + y^2 \leq 4 $ and y $<x u done the circle part y<x, y = x is a line satisfying (0,0) (1,1) (2,2) (3,3), etc y<x so shade the bottom (using the vertical line test - draw vertical line on the curve, since less than, we choose the bottom) NB: its less than but NOT EQUAL TO, hence the...

Quadratic = x^2 - (sum of roots)x + (product of roots) (remember ur minus!) u are absolutely correct, nothing beats factorisation