[Integration] Which recurrence formulas are in the syllabus? (1 Viewer)

[UnrealAnchovies]

My teacher said that only formulas for (no clue how to use latex): cos^(n)x, sin^(n)x and x^(n)e^x are in the syllabus. But I was just going through some 1990s papers, and noticed that other types seem to be present.

So, are there more recurrence formulas then those 3 mentioned above? or has the syllabus changed since then?

 

[Bored Of Fail]

http://archives.math.utk.edu/visual.calculus/4/index.html
this visual calculus site is a good site for integration, I am pretty sure from memory they have exercise that derive alot of reduction formulas ( with some outside 4unit as it involves hyperbolic trig functions which are not covered in 4unit)

 

[Bored Of Fail]

integrals like sin ^ n (x) cos ^m (x) where there are two powers to reduce are not in 4unit, im pretty sure

 

[Trebla]

ANY recurrence formula is examinable provided that the very function (integrand) you are integrating is within the Extension 1/Extension 2 syllabus (i.e. algebraic functions, trigonometric functions, exponential functions, logarithmic functions, inverse trigonometric functions).

Most exam questions will give you a reduction formula and you'll be asked to prove something from it, so you don't need to memorise any of them. Just be familiar with the techniques to derive a recurrence relation.

 

[UnrealAnchovies]

Thanks for the responses.

I think I'll have to learn the other ones. The only recurrence formula I know are those 3 I mentioned above.

 

[Bored Of Fail]

that site is also pretty good for differentiation and also covers a fair few other topics

 

[UnrealAnchovies]

So long as It has a few decent questions I'll check it out.

Thanks though!

 

[Bored Of Fail]

if you can do all the questions on that site you will be well on the way to smash maths

 

[annabackwards]

ANY recurrence formula is examinable provided that the very function (integrand) you are integrating is within the Extension 1/Extension 2 syllabus (i.e. algebraic functions, trigonometric functions, exponential functions, logarithmic functions, inverse trigonometric functions).

Most exam questions will give you a reduction formula and you'll be asked to prove something from it, so you don't need to memorise any of them. Just be familiar with the techniques to derive a recurrence relation.

+1

The sec, tan and cot reccurence formulas turn up a few times too. But yeah, learn the process of deriving them and don't just memorise!

 

[Aquawhite]

+1

The sec, tan and cot reccurence formulas turn up a few times too. But yeah, learn the process of deriving them and don't just memorise!

Yeah, there's no practical way to memorise them properly... and as you probably saw from the 2010 Paper, Question 8, the recurrence formula can be quite complex and involve a few factors and a number of steps to manipulate.

 

[cutemouse]

The ones involving factorials are my favourite

 

[Gussy Booo]

As stated in the previous posts, there are many. But even more so, they can be manipulated in ways that can make them quite hard :|
Yes, the 2010 Q8 was a doosey. My best advice is to do past papers. Go to questions 6,7,8 and do as many as you can. With trigonometry you always have the typical "split the powers" in order to obtain some sort of progression. Combinations of functions would require you to understand which substitution to make via integration by parts. I tend to rely on L.I.A.T.E.

L - Log
I - Inverse
A - Algebra
T - Trigonometry
E - Exponential.

The letter which comes before another is usually the one that stays within the integrand, whilst the letter after is usually substituted. This is too hard to explain over the forums. But what I'm trying to get at is that there are many recurrence formulas, and the best way to overcome them all is to do as many as you can.

 

[UnrealAnchovies]

I haven't actually memorized them. It's just familiarizing myself with the process of deriving them and applying this to a few practice questions.

I've never encountered any that involve the factorial sign tbh - a clear indication I'm missing a few. >.<

 

[iSplicer]

I haven't actually memorized them. It's just familiarizing myself with the process of deriving them and applying this to a few practice questions.

I've never encountered any that involve the factorial sign tbh - a clear indication I'm missing a few. >.<

There are some nice questions in Terry Lee that deal with this sort of thing.

 

[Gussy Booo]

I haven't actually memorized them. It's just familiarizing myself with the process of deriving them and applying this to a few practice questions.

I've never encountered any that involve the factorial sign tbh - a clear indication I'm missing a few. >.<

Past papers is the key :]