I don't know if this will help, but from the definiton of g(x),
I'm having difficulty with part (ii) of the first link.
I used the result from part (i) and was able to get g(Tb)-g(Ta)- integral from Ta to Tb of g(x)/x dx...
I noticed that the g(Ta)-g(Tb) terms cancel and i'm only left with the integral term.
I used by parts on the integral term with u=g(x) , du= g'(x) dv= 1/xdx, v= lnx.
My problem is that I can't seem to get rid of the final integral term. Any help would greatly be appreciated.
I'm also stuck with the question in the second image, I believe that this questions requires me to apply my result from part(ii)?
Question part(ii) ImageShack® - Online Photo and Video Hosting
ImageShack® - Online Photo and Video Hosting
Thank you very much, I was able to complete part(ii).
I'm now a little stuck on part(iii),
I was able to seperate the integral and use change of variables where u=ax and z=bx.
Then applying the mean value theorem for integrals from similarily from part (ii),
where c belongs to [a,b]
I'm stuck at this step, I'm having a hard time relating the 2nd term to the required f(t)/t integral.