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Re: HSC 2013 4U Marathon ah, I did it without substitution by completing the square and converting to partial fractions. It should be able to be integated into inverse tans ? dunno if it works lol...

Re: HSC 2013 4U Marathon not sure if I'm on the right track, but does the answer happen to have a lot of \sqrt{24}?

oops that's right, I misread it I take that back lol

Don't get too used to it :p Can barely answer the other 99% of sy's questions Ah that's a much easier substitution, thanks :)

Not exactly, it depends on the relative gaps between internal rankings

Re: HSC 2013 4U Marathon \begin{align*}x&=\tan^4\theta\\dx&=4\tan^3\theta\sec^2\theta d\theta\\ \frac{1}{1+\sqrt{x}}&=\cos^2\theta\\\int {\frac{dx}{1+\sqrt{x}}}&=\int\cos^2\theta\cdot 4\tan^3\theta\sec^2\theta d\theta\\&=4\int \tan^3\theta d\theta\\&=4\int\left (...

Re: HSC 2013 4U Marathon Evaluate \int_{0}^{1}\frac{x^2+3x+2}{x^2-x+1}dx

http://shop.cottonon.com/shop/rubi/ is pretty decent

The graphs that you are expected to draw in exam conditions will mostly likely have reasonable scale, i.e. a question won't ask you to draw something with a y-intercept of (0,-947) A good starting point is to use the horizontal lines of the exam booklet/pad to work out your scale, and you can...

really? you mean \int\frac{3\tan{x}}{x^2}dx ? I highly doubt it... unless I'm reading it wrong

That is definitely not a 2U integration question And its ln(x+4) + C

^

Assuming that you integrated and subbed in the limits from 0 to 2 correctly of course.

The graph is odd so perhaps you forgot to times the area by two?

I would say around hundreds?

basically just polynomials?

Ah fair enough only thing I could think of that works

Personally I find that it helps if you do mentally do circle geo questions during reading time (after you quickly flick through the paper) and hopefully you would already have a general idea of the proof beforehand so you only have to worry about expressing/writing it down on paper. Otherwise I...

If you need help in English, a tutor is extremely effective imo. Maybe find another one if you're not happy with your current one? Try the BOS classified section.

I stand corrected then, thank you for your correction Guess my whole argument fell apart !!1! :(