HSC Stuff > HSC Mathematics Extension 2

Nagisa Maths Thread

<< < (18/18)

Planck's constant:

--- Quote from: Clifford on December 29, 2012, 04:12:34 am ---Try a double substitution, firstly let to produce a new integral, then secondly let (or whatever letter you want to use for your second substitution) to simplify it again.

If you have any trouble with that I can write a full solution for you :)

--- End quote ---


Yes. In effect it is the single substitution u= sqrt(4x+1).
Everything goes nicely, and the answer pops out in a single step, as long as you can recognise the integral as that of arctanh(u)

polar:
here you go. this solution doesn't use the arctanh function though, so it's a bit longer

Spoiler

Planck's constant:

--- Quote from: polar on December 29, 2012, 11:42:50 am ---here you go. this solution doesn't use the arctanh function though, so it's a bit longer

Spoiler
--- End quote ---


Yes, that's right.
But you can stop 5 steps earlier if you recognise arctanh, else you end up deriving a formula for arctanh from first principles :)

Phy124:

--- Quote from: argonaut on December 29, 2012, 11:11:51 am ---
Yes. In effect it is the single substitution u= sqrt(4x+1).
Everything goes nicely, and the answer pops out in a single step, as long as you can recognise the integral as that of arctanh(u)

--- End quote ---

Yeah that's quite right, I just found teaching these sort of substitutions in multiple steps reduced errors made by the students, do whatever you feel most comfortable with :)

Nagisa:
thanks guys, good to see u making an effort argonaut.

Navigation

[0] Message Index

[*] Previous page