Struggling with Reverse chain rule, can I just use substitution instead?

I've been revising for my A level maths and I'm getting really stuck on doing more complex reverse chain rule questions. Is it actually necessary for me to know it inside out or could I just use substitution instead? I know substitution takes longer, I just tend to make mistakes when using reverse. If anyone has any advice that would be great thanks!

Reply 1

cersef

13

i dont even remember integration rn but my advice would be to master the reverse chain rule
we still have two months till the first exam and i believe it’s worth it, especially if it saves time. you only get over a minute per mark.
however, i’m not saying to never use substitution, but it’d probably be super helpful to be comfortable with all methods of integration :]

Reply 2

Muttley79

20

Original post by Gregory05

I've been revising for my A level maths and I'm getting really stuck on doing more complex reverse chain rule questions. Is it actually necessary for me to know it inside out or could I just use substitution instead? I know substitution takes longer, I just tend to make mistakes when using reverse. If anyone has any advice that would be great thanks!

Use substitution if you need to - it's safer. No point in saving time if you get it wrong.

Reply 3

DFranklin

18

Original post by Gregory05

I've been revising for my A level maths and I'm getting really stuck on doing more complex reverse chain rule questions. Is it actually necessary for me to know it inside out or could I just use substitution instead? I know substitution takes longer, I just tend to make mistakes when using reverse. If anyone has any advice that would be great thanks!

There's absolutely nothing wrong with using substitution instead of the reverse chain rule.

In fact the general consensus amongst the graduates on here is that the reverse chain rule causes a lot more problems than it solves.

That said, it does save time if it's *obvious* to you how to use it, and in particular it *is* worth knowing how to write down the integral of f(ax+b) in terms of the integral of f(x).

(edited 1 year ago)

Reply 4

Notnek

21

Original post by Gregory05

I've been revising for my A level maths and I'm getting really stuck on doing more complex reverse chain rule questions. Is it actually necessary for me to know it inside out or could I just use substitution instead? I know substitution takes longer, I just tend to make mistakes when using reverse. If anyone has any advice that would be great thanks!

The most important thing is that you can recognise the function/derivative patterns so that you can apply either method.

E.g. if you have

\int 3x \ e^{x^2} \ dx

then you need to notice that 3x is close to the derivative of x^2 so substituting

u=x^2

or considering the derivative of

e^{x^2}

will work.

You may find that with lots of substitution practice, you could pick up some of these reversal methods naturally.

(edited 1 year ago)

Reply 5

Gregory05

OP

6

Thank you! I'll try to get a good idea of it but I just feel more secure when doing substitution :smile:

Original post by DFranklin

There's absolutely nothing wrong with using substitution instead of the reverse chain rule.

In fact the general consensus amongst the graduates on here is that the reverse chain rule causes a lot more problems than it solves.

That said, it does save time if it's *obvious* to you how to use it, and in particular it *is* worth knowing how to write down the integral of f(ax+b) in terms of the integral of f(x).

Reply 6

davros

16

Original post by Gregory05

I've been revising for my A level maths and I'm getting really stuck on doing more complex reverse chain rule questions. Is it actually necessary for me to know it inside out or could I just use substitution instead? I know substitution takes longer, I just tend to make mistakes when using reverse. If anyone has any advice that would be great thanks!

To turn the question around, what do you mean by "reverse chain rule questions"? Are the questions concerned asking you to use "reverse chain rule", or do they say "evaluate the integral"? If it's the latter, then substitution is almost always the safe way to go, unless the integral is so "obvious" that you can spot what the answer is going to be in the first place!

(The phrase "reverse chain rule" is just a horrible recent invention that never used to appear in calculus books anywhere - it should properly be called the "reverse chain trick" since it only applies in very special cases, and the chances of meeting an integral "in real life" where it can be safely used are extremely small. Then again, the chances of meeting any integral in real life are extremely small :biggrin:

)

Reply 7

davros

16

Original post by Gregory05

Thank you! I'll try to get a good idea of it but I just feel more secure when doing substitution :smile:

That's hardly surprising, since substitution is a long-established technique of integration which you can practise on any integral (not necessarily productively!), whereas the so-called "reverse chain rule" is nothing of the sort - it's a combination of implicit substitution and educated guesswork that can only be used when the integral has a particular form - and if you're good enough to spot that form then you're probably very good at substitutions anyway!

Struggling with Reverse chain rule, can I just use substitution instead?

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