HSC Tips - Integration (1 Viewer)

[McLake]

OK, number 5

Tips for Intergration:
- There are seven main types:
-- Standard (3U) Integration
-- Integration by substitution
-- Integration by parts
-- Completing the square (Tan Integration)
-- Trig Integration
-- T Formula Integration
-- Partial Fractions

- Almost always all of question 1.

- Often the method is stated.

- REMEMBER TO WRITE "+ C" WHEN RELEVENT

- Familurise yourself with tricky "recursion" questions (will post some of those in another thread)

 

[ezzy85]

first check if the bottom can be factorised, then consider the above methods if it cant.

 

[Affinity]

priorities(the order to look for in general)

0.)obvious definite integrals eg even and odd functions.
1.)standard form
2.)direct substitutions ( f'(g(x)*g'(x) integrals)
3.)inverse substitutions ( x = arcsin(t) etc)
4.)Complete square and/or partial fractions
5.)By Parts.
6.)T or other weird and messy subs. avoid if possible.

mastering integration is a prerequisite for doing well in the next two topics.

 

[freaking_out]

mastering integration is a prerequisite for doing well in the next two topics

yeah, i learnt that the hard way. :mad1:

 

[punk0rz]

recursion

is this just another name for reduction ?
i havent heard it put like that before

 

[Affinity]

recursion is more precise than reduction in this case.

 

[freaking_out]

Originally posted by Affinity
priorities(the order to look for in general)...

3.)inverse substitutions ( x = arcsin(t) etc)

what?? how/when can u use "let x=arcsin(t)"?? the only similiar thing to this i know is let t=tan(x/2) or let x=sinA to cancel out square roots.

 

[ND]

Originally posted by freaking_out
what?? how/when can u use "let x=arcsin(t)"?? the only similiar thing to this i know is let t=tan(x/2) or let x=sinA to cancel out square roots.

Sometimes it's just easier that way. A simple example is I((sinx)/((cosx)^2)dx, most people should be able to do this in their head, but if not, let cosx=u (i.e. x = arccos(u)).

 

[Excalibur]

WHATs the point of thinkin up substitutions when we have the wonderful differential method!!!!!!!! look it up ppl it is awesome, if you think there's nothin easyier than complex no. i challenge you!!!

 

[ND]

Originally posted by Excalibur
WHATs the point of thinkin up substitutions when we have the wonderful differential method!!!!!!!! look it up ppl it is awesome, if you think there's nothin easyier than complex no. i challenge you!!!

Yep, anyone who doesn't know this method should look at OLDMAN's site.

 

[ezzy85]

what his site again?

 

[McLake]

Originally posted by ezzy85
what his site again?

http://www.users.bigpond.net.au/gotmaths/

 

[Grizzly]

Yo guys use the "LIATE" Technique when doing integration by parts ?
e.g, what to let u', u, v', v

 

[Giant Lobster]

that "differential" method, isnt it just common sense? hehe my friends and i call it integration by inspection

whats this liate method?

 

[freaking_out]

Originally posted by Grizzly
Yo guys use the "LIATE" Technique when doing integration by parts ?
e.g, what to let u', u, v', v

i never heard of such a method. :s

 

[KeypadSDM]

Weird, neither have I.

The only ways I ever did integration was by parts or direct integration (integration by inspection).

There's rarely a problem you can't solve either way.

And yes, you can do the square root ones by parts, it just takes a little longer. (Plus it also gives you a feeling for all the little fiddly bits in 4 unit, practice at that should be mandatory)

 

[DcM]

i heard that in the HSC if u answered like the first few qs with the + C
then u dun need to later on...cos they supposingly assume u know that its + C..
is this true?

 

[CM_Tutor]

Originally posted by DcM
i heard that in the HSC if u answered like the first few qs with the + C
then u dun need to later on...cos they supposingly assume u know that its + C..
is this true?

No.

 

[freaking_out]

Originally posted by DcM
i heard that in the HSC if u answered like the first few qs with the + C
then u dun need to later on...cos they supposingly assume u know that its + C..
is this true?

yeah, i heard that as well...i.e that if in the first quesiton u put +C, and u forget it for the rest of the question, then they don't mark u down.

 

[CM_Tutor]

My answer remains no, and here's why: There are very few questions 'later on' in an HSC that will invove integration finding an indefinite integral, where you will not need to then find the constant C. Get into the habit of always writing the '+ C'm as you don't know when you're going to need it.

Also, you write in different booklets as they are marked by different people, so no one marking a Q 5 will go back and check if you added the '+ C' in earlier questions.