Question: Are we assuming this is integrable? Because if for any , it is not integrable.
Thanks to Slip Eternal for a correct solution. Mine is quite similar, but doesn't involve splitting up the interval:
Let
(1)
Let u = 6 - x. Then
Neaten up the limits on the integration and switch the dummy variable from u back to x gives:
(2)
Add lines (1) and (2):
And thus I = 1.
-Dan