Reverse Chain Rule ? (1 Viewer)

[accio.brain]

Has anyone been taught the reverse chain rule for integration?
I asked my teacher about it cos we never learnt it, & he said they don't teach it anymore cause the syllabus changed or something. Seems kinda weird to get rid of a formula but I'm just checking, please. Thanks :]

 

[shaon0]

Has anyone been taught the reverse chain rule for integration?
I asked my teacher about it cos we never learnt it, & he said they don't teach it anymore cause the syllabus changed or something. Seems kinda weird to get rid of a formula but I'm just checking, please. Thanks :]

its not a formula. You don't have to learn it, it's just a precursor to integration by substitution.

 

[alakazimmy]

The reverse chain rule is integration by parts. It's in the 4u course.

 

[shaon0]

The reverse chain rule is integration by parts. It's in the 4u course.

isn't reverse chain rule the form where the derivative of a certain part of the integral is apparent without using substitution?
ie. S 2x(x^2-1) dx

 

[alakazimmy]

oh, oops, i was thinking of reverse product rule.
Yea, you pull a derivative out. It's basically substitution for the lazy.

 

[Trebla]

Has anyone been taught the reverse chain rule for integration?
I asked my teacher about it cos we never learnt it, & he said they don't teach it anymore cause the syllabus changed or something. Seems kinda weird to get rid of a formula but I'm just checking, please. Thanks :]

It has always been part of the syllabus, it just hasn't been explicitly mentioned. It basically is:

You are certainly allowed to use it and it may often be quicker and less error prone than a formal substitution.
e.g.

 

[possessionless]

didnt even know it existed LOL

 

[annabackwards]

I learnt the reverse chain rule in 2U math, although we hardly ever used it oO

 

[youngminii]

Don't use it. It's just a way to skip substitution for relatively easy substitution questions.
Don't use it. You'll just make silly mistakes and lose marks and kick yourself and say to yourself, "Damn, I should've listened to that youngminii guy."

 

[withoutaface]

Don't use it. It's just a way to skip substitution for relatively easy substitution questions.
Don't use it. You'll just make silly mistakes and lose marks and kick yourself and say to yourself, "Damn, I should've listened to that youngminii guy."

Use it. It will make this guy angry.

 

[accio.brain]

haha. kk, thanks

 

[Uncle]

I learnt the reverse chain rule in 2U math, although we hardly ever used it oO

Remember not the formula but the process.

Don't use it. It's just a way to skip substitution for relatively easy substitution questions.
Don't use it. You'll just make silly mistakes and lose marks and kick yourself and say to yourself, "Damn, I should've listened to that youngminii guy."

As an ENGINEERING student, I have found it MORE practical to integrate via inspection rather than substitution.
Even in conjunction with integrating by parts.
Even with more than one variable.
Makes 3-unit integral functions look like simple 2-unit anti-derivatives.

I have made little errors out of all the problems I have solved.

Have a crack at these:
http://community.boredofstudies.org/12/mathematics/179888/challenge.html
See how long it takes you to solve them via substitution compared to inspection.

 

[youngminii]

Jeez, it doesn't waste that much time + you've still said you lost a few marks.
But I guess if you're completely pro at it, reverse chain rule is better time-wise, if you're 100% confident you can do it without making a mistake.

Also that thread is nice but you don't have to do integration by parts in ANY of them ==;;

 

[Bacchus]

Jeez, it doesn't waste that much time + you've still said you lost a few marks.
But I guess if you're completely pro at it, reverse chain rule is better time-wise, if you're 100% confident you can do it without making a mistake.

Also that thread is nice but you don't have to do integration by parts in ANY of them ==;;

I agree with Andrew. For someone like me who makes tonnes of silly errors, doing it by sub is the easiest way.

 

[youngminii]

I agree with Andrew. For someone like me who makes tonnes of silly errors, doing it by sub is the easiest way.

Who are you and how do you know my name WTF?

I'm sticking to substitution

 

[joben]

'reverse chain rule' can be found in the cambridge y11 3 unit (fat brown book).

 

[Trebla]

Don't use it. It's just a way to skip substitution for relatively easy substitution questions.
Don't use it. You'll just make silly mistakes and lose marks and kick yourself and say to yourself, "Damn, I should've listened to that youngminii guy."

I disagree. I think you are more likely to make silly mistakes in subsutition than in reverse chain rule (provided you are effective at either). In a formal substitution you have to remember to substitute back into original variable or change limits. Forgetting to do this is a common silly mistake. You don't have to worry about ANY of these in the reverse chain rule.

 

[Uncle]

Time was wasted when the lecturer integrates via substitution with respect to x:

[maths]\frac{x^{3}}{\sqrt{x^{4}+y^{2}}}[/maths]

which is also:

[maths]{x^{3}}.(x^{4}+y^{2})^{-\frac{1}{2}}[/maths]

Then integrating via inspection to get:

[maths]2.\frac{1}{4}.(x^{4}+y^{2})^{\frac{1}{2}}+C[/maths]

2 is to "cancel out" the constant term after differentiating the inside chain rule w.r.t. x
1/4 is to "cancel out" the power which comes down when you pretend to differentiate the integral again.

[maths]\frac{1}{2}.(x^{4}+y^{2})^{\frac{1}{2}}+C[/maths]

If you have a bit more time differentiate the integral w.r.t. x to check.

Simple.
See the pattern?

Also makes the quotient rule obsolete, which I forgot.
The quotient rule is just a derivation of the product rule with the chain rule.

Jeez, it doesn't waste that much time + you've still said you lost a few marks.
But I guess if you're completely pro at it, reverse chain rule is better time-wise, if you're 100% confident you can do it without making a mistake.

Also that thread is nice but you don't have to do integration by parts in ANY of them ==;;

Time wasted?
How about exams?
Have you even bothered to check this thread?
http://community.boredofstudies.org/12/mathematics/179888/challenge.html\
Try solving them all in under 10 minutes using either method (substitution or inspection).

I agree with Andrew. For someone like me who makes tonnes of silly errors, doing it by sub is the easiest way.

Because you haven't worked on enough integrals and/or your brain isn't capable enough to solve by inspection.
With experience which I gained from solving countless integrals, integration via substitution will become obsolete for 'reverse chain rule integrals'.

I disagree. I think you are more likely to make silly mistakes in subsutition than in reverse chain rule (provided you are effective at either). In a formal substitution you have to remember to substitute back into original variable or change limits. Forgetting to do this is a common silly mistake. You don't have to worry about ANY of these in the reverse chain rule.

As he said, especially with the limits.

 

[Michaelmoo]

Yer its not in the syllabus, but you can still use it as a little trick in some integration questions. I'd actually advise you use it if you can learn to use it without silly mistakes.

In the HSC, you WILL get at least one 3 mark integration question. This method could allow you to pump 3 marks in 10 seconds rather than 40 seconds or something.