Terry Lee's 'mental method' for partial fractions allowed? (1 Viewer)

[Sanical]

Are we allowed to use his mental method in exam, as in show no working at all?
For example, can you straight out say:



If you were to show working, you'd have to sub in numbers and equate coefficients.

 

[IamBread]

Most questions will say "show this = this. Then use it to integrate this" so it's best to show your working.

 

[Carrotsticks]

If the question is:

Integrate *expression requiring partial fractions*

Then it is okay to use it.

If as Iambread said, it says:

Show that XXX = YYY, hence integrate XXX

Then you must do it using the coefficients method (or substitution method).

 

[study-freak]

I reckon you can write it as a claim and then prove it by making RHS into LHS (much easier if you are sure that your RHS is correct).

 

[Trebla]

Are we allowed to use his mental method in exam, as in show no working at all?
For example, can you straight out say:



If you were to show working, you'd have to sub in numbers and equate coefficients.

There is nothing overly special about this 'mental method'. If you look carefully at how it is proved using a limit argument, it's no different to the substitution approach. The only reason it appears simpler is because this method involves division of numbers (which can simplify nicely) rather than multiplication through the substitution/equating coefficients approach.

In an exam, if you just wrote the correct answer (provided the question is not a proof type one) then you will get full marks. However, keep in mind this carries the risk of getting zero if the answer is wrong without any working provided.

Note - one way you could do this question would be by nice manipulation (note this doesn't always work as nicely):

 

[Sanical]

Most questions will say "show this = this. Then use it to integrate this" so it's best to show your working.

If the question is:

Integrate *expression requiring partial fractions*

Then it is okay to use it.

If as Iambread said, it says:

Show that XXX = YYY, hence integrate XXX

Then you must do it using the coefficients method (or substitution method).

Yeah, I guess I'll write out the steps

I reckon you can write it as a claim and then prove it by making RHS into LHS (much easier if you are sure that your RHS is correct).

May as well just do it by showing working out in first place

There is nothing overly special about this 'mental method'. If you look carefully at how it is proved using a limit argument, it's no different to the substitution approach. The only reason it appears simpler is because this method involves division of numbers (which can simplify nicely) rather than multiplication through the substitution/equating coefficients approach.

In an exam, if you just wrote the correct answer (provided the question is not a proof type one) then you will get full marks. However, keep in mind this carries the risk of getting zero if the answer is wrong without any working provided.

Note - one way you could do this question would be by nice manipulation (note this doesn't always work as nicely):

:O
So cool When would you know when to use this?

 

[AAEldar]

So cool When would you know when to use this?

It won't work all the time, as Trebla said, but you'd recognize it in that example by seeing that adding an to the numerator will make you be able to cancel out the in one of the denominators. Then you must also subtract that and you see it factorizes and cancels the other one.

 

[Sanical]

It won't work all the time, as Trebla said, but you'd recognize it in that example by seeing that adding an to the numerator will make you be able to cancel out the in one of the denominators. Then you must also subtract that and you see it factorizes and cancels the other one.

Ah, ok thanks