nightweaver066
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Re: HSC 2012 Marathon
How about..
How about..
k! - 1Mind if I extend the question a bit?
Herp derp let z=9sintheta because obviously there's no geometric way of doing it =pHow about..
spoiler alert noob!herp derp let z=9sintheta because obviously there's no geometric way of doing it =p
yeh quadrants of circles dont existHerp derp let z=9sintheta because obviously there's no geometric way of doing it =p
Don't really like how you had dx = du/5x^4.... mixing X and U...<a href="http://www.codecogs.com/eqnedit.php?latex=\int \frac{x^4}{1@plus;x^{10}} \textup{dx} ~\\ Let ~u = x^5 \\ \frac{du}{dx}= 5x^4 \\dx=\frac{du}{5x^4} \\ \frac{1}{5}\int \frac{1}{1@plus;u^2}~ \textup{dx} = \frac{1}{5}\tan^{-1}u @plus; \textup{C} , ~since~ u ~= x^5 \\\\ \frac{1}{5}\tan^{-1}x^5 @plus; \textup{C}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\int \frac{x^4}{1+x^{10}} \textup{dx} ~\\ Let ~u = x^5 \\ \frac{du}{dx}= 5x^4 \\dx=\frac{du}{5x^4} \\ \frac{1}{5}\int \frac{1}{1+u^2}~ \textup{dx} = \frac{1}{5}\tan^{-1}u + \textup{C} , ~since~ u ~= x^5 \\\\ \frac{1}{5}\tan^{-1}x^5 + \textup{C}" title="\int \frac{x^4}{1+x^{10}} \textup{dx} ~\\ Let ~u = x^5 \\ \frac{du}{dx}= 5x^4 \\dx=\frac{du}{5x^4} \\ \frac{1}{5}\int \frac{1}{1+u^2}~ \textup{dx} = \frac{1}{5}\tan^{-1}u + \textup{C} , ~since~ u ~= x^5 \\\\ \frac{1}{5}\tan^{-1}x^5 + \textup{C}" /></a>
I've always done it like that :SDon't really like how you had dx = du/5x^4.... mixing X and U...
Stuck on 3 and 4, i tried using v^2=n^2(a^2+x^2) and -n^2 . xJohn Fitzpatrick 3U Mathematics 25(c) Question 3
A particle movies in a straight line. At time t seconds, its displacement x cm from a fixed poin O in the line is given by x=5sin((pi/2)T + pi/6). Express the acceleration in terms of x only and hence show that the motion is simple harmonic. Find:
iii) The speed when x=-2+1/2
iv) the acceleration when x = -2 + 1/2
Best to avoid it.I've always done it like that :S
Who said anything about a circle? And quadrants?yeh quadrants of circles dont exist
It's v^2=n^2(a^2-x^2)Stuck on 3 and 4, i tried using v^2=n^2(a^2+x^2) and -n^2 . x
Oooh, if you could find it, can you post it again. A nice question that I remember you posting was how to integrate 1/1+tan^n(x) between 0 and pi/2 but that needs 4U techniques...Best to avoid it.
du = 5x^4 dx would have sufficed.
Also, I remember I made a nice integration question a while ago and I posted it up somewhere...
It basically was a way of evaluating:
Without actually knowing the integral of ln(x).
not sure if srs -_-Who said anything about a circle? And quadrants?
This isn't that hard is it? The left of the e is just the derivative of the exponent divided by 5.Here's a really tricky one,
Just looking at that wouldnt you make u = x^5 + 5x^2-5x ?Here's a really tricky one,
Not necessarily.Oooh, if you could find it, can you post it again. A nice question that I remember you posting was how to integrate 1/1+tan^n(x) between 0 and pi/2 but that needs 4U techniques...
Yep. If you can though, try and learn to do these sorts of things without having to let u=whatever. Something like this you can just recognise after you do a lot of them which saves a lot of time in tests.Just looking at that wouldnt you make u = x^5 + 5x^2-5x ?
Yep.Just looking at that wouldnt you make u = x^5 + 5x^2-5x ?