4u integration (2 Viewers)

[Susu123]

when i want to use this integral formula in the ext 2 hsc, if it comes up, am i supposed to derive it or can i just memorise this and use it

 

[liamkk112]

when i want to use this integral formula in the ext 2 hsc, if it comes up, am i supposed to derive it or can i just memorise this and use it
View attachment 42911

well im pretty sure this will not come up on the hsc since it's out of syllabus, the way you derive it is through hyperbolic trig substitutions but obv thats not in the syllabus. if on the very rare occassion that you're asked it on the hsc you can always quote the result and differentiate the log to show the integral is correct, but again u prob won't be asked this

 

[Average Boreduser]

well im pretty sure this will not come up on the hsc since it's out of syllabus, the way you derive it is through hyperbolic trig substitutions but obv thats not in the syllabus. if on the very rare occassion that you're asked it on the hsc you can always quote the result and differentiate the log to show the integral is correct, but again u prob won't be asked this

wait can't you derive it using trig sub?

 

[Susu123]

well im pretty sure this will not come up on the hsc since it's out of syllabus, the way you derive it is through hyperbolic trig substitutions but obv thats not in the syllabus. if on the very rare occassion that you're asked it on the hsc you can always quote the result and differentiate the log to show the integral is correct, but again u prob won't be asked this

ahh ok makes sense, thanks! i might get it in trails, since my school expects me to know this, so ill just confirm that with my teacher

 

[liamkk112]

wait can't you derive it using trig sub?

u can try but im not sure it would work, u get some difficult integrals that might be impossible/super hard
hyperbolic trig is the standard way to do it tho

 

[liamkk112]

ahh ok makes sense, thanks! i might get it in trails, since my school expects me to know this, so ill just confirm that with my teacher

if it’s in internals you’re probably fine just quoting the result, but it’s good to double check obv yea

 

[liamkk112]

u can try but im not sure it would work, u get some difficult integrals that might be impossible/super hard
hyperbolic trig is the standard way to do it tho

actually u can do them but u need to know integral of sec, which is annoying

 

[Luukas.2]

They were standard integrals on the old syllabus, but that's going back a way - see page 16 of the 2001 paper accessible from https://educationstandards.nsw.edu....matics/mathematics-2001-hsc-exam-pack-archive, for example

 

[Susu123]

They were standard integrals on the old syllabus, but that's going back a way - see page 16 of the 2001 paper accessible from https://educationstandards.nsw.edu....matics/mathematics-2001-hsc-exam-pack-archive, for example

yeah i saw them in a bunch of older paper so i was wondering lol thanks

 

[QualityHSC]

You can also reverse engineer the result by multiplying both num and denom by x/sqrt(x^2+a^2) + 1

 

[Trebla]

It’s not in syllabus anymore so at best you will be asked to derive the result (you shouldn’t be quoting it) under today’s syllabus. It can be derived normally by trig substitution. This is for the external HSC btw, but your school can make up their own rules on what is allowed for internals which may or may not align to the actual HSC.