Submitted by Anonymous (not verified) on
Why can you not rearrange the equation in 4ii -- so i(n)=-(m+1/n+1)i(n+1)
then sub in your values for m and n in 4iii
for example:
the integral between 1 and 0 of x^2(lnx)^2 = the integral of -3/2 x^2(lnx)
where m=2 and n+1=2.
I know this doesn't give the right answer but I don't know why. (Also I know it should be divided by 2 but it was just an example).
Basically I'm setting (xlnx)^2 as i(n+1) so I'm essentially repeating the steps done in 4ii.
Is it possible both series converge to the same limit?
I would appreciate any help
May help. Don't fully understand the question
Submitted by Rayman (not verified) on
That rearrangement is fine but the question in 4ii asks us to evaluate $I_n$. So we don't really want to have to express it in terms of another integral. Which is why we use recursion to express $I_n$ in terms of $n$, $m$ and $I_0$ where we can work out $I_0$ and then not have to worry about other integrals as $I_n$ is expressed nicely in terms of $n$ and $m$.
Once you've done that. You can work out $\int {x^2({\ln x})^2} \mathrm{d}x$ quite comfortably without having to write it in terms of another integral you would have to work out.
Hope that helps.
thank you
Submitted by O________O (not verified) on
thank you