Question on double integral

[randomkido]

Hi guys, I have a question regarding the double integral calculation in the last line below (the stuff preceding the last line is just for background):

What I get is 1/2 T^3 . Can anyone explain why the widely popular answer (which is used in many literature) is 1/3 T^3 ?

Thank you!

 

[Zhenfeng Leung]

Break the integral into to two parts.
Then you will get the right answer.

\(\int_{0}^{T} (\int_{0}^{s} t \ dt + \int_{s}^{T} s \ dt) \ ds\)

 

[randomkido]

Thanks a lot!