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x = sec(u) is fine when x is no less than 1 (or no greater than minus 1), else there might be problems... for example int [-1 to 1] 1/x^2 does not exist but if you substitute x=sec(u) you get int [pi to 0] sin(x) = -cos(0) + cos(pi) = -2 yeah you can use the domain -3pi/2 and -pi/2, you just...

tan substitutions work perfectly, remember you don't get close to any funny points since x = tan(u) ----> x varies over all reals, but tan(u) only has be defined for u in (-pi/2,pi/2) and for this interval secant is also fine. there might potentially be problems with sec substitutions

As with most topics it's about looking at things the right way. Build your intuition starting from easy questions

Sit down and think about it until it makes sense

once you get it back into [x(x^2+4)^(1/2)]/2 + 2 log(x + (x^2 + 4)^(1/2)) you can see that it doesn't really matter. hmm the tan substitution is not that bad, it's a one to one function. you can start with x = -2tan(u) and you will end up with the same thing.

1/2 ( x sqrt (x^2 + 1) - log( x + sqrt (x^2 + 1)) )

might be better: x = [e^{t} - e^{-t}]/2 then your integral = int [e^{2t} + e^{-2t} - 2]/4 dt [the extra bits cancel.] = e^{2t}/8 -e^{-2t}/8 - t/2 = x(sqrt(x^2+1))/2 - log(x + sqrt(x^2 + 1))/2 etc. For those who are interested: notice on your calculator there's a hyp button and if...

calculators save you no time in the 4 unit exam

If you claim that PQRS is 15 by 6 then something is wrong.

It could be included as an actual number

is geoff ball still there? thought he retired long ago.

for example when my UAI was calculated the subjects taken were: English advance (2 units) Physics (2units) Chemistry (2 units) Mathematics extension 1 (2 units) Mathematics extension 2 (2 units)

when you do 4 units your maths ext 1 and ext 2 marks are weighted as a 2unit course for UAI calculation

Go train for olympiads,

hint: cos(3t)-cos(4t)=2sin(7t/2)sin(t/2)

they are the same shit ... and same as the bachelors program. finance hmm not sure.. I think it's not that useful, might as well get a job.

really depends on what you do exactly... on one end you ahve hard core numerical computing in C++ and on the other end some easy peasy spreadsheet work..

And based on that experience I am advising against actuarial studies.. one might as well do accounting + maths

screw actuarial studies degrees.. do maths and take exams externally

Not quite sure about that...