Some inquisitive students have asked me before, how the MF15 integration formulas come about. I thought I should share it too then.
So we want to 
and yes, we know the formula can be plugged directly… but what if we want to avoid the formula. Now actually, the trick here involves your trigonometry identities, along with substitution methods. We have a 
here, so we only know one trigo identity that involves and that is 
. Hmmm, so my approach here will be to let 
. We will see shortly why I chose to put a 2 and that using 
or 
will make no difference. You can try them yourself!
Credits: Wikipedia
lets first find that 
If you notice, this explains why there is a need for us to introduce 
instead of just .
Having
allows us to simplify it to
We have 
Finally, 
That was long! But i hope it give you some insights to the formulas.
