Missing pictures and wrong solution?
I flagged the new solution as good. I know some students get hung up on some of these geometrical (shell vs. disks vs. washers) ideas so if there were to be any changes, I'd recommend an extra graphic like in solution 1 that kind of shows a sample washer. It's not a big deal though.
Unfortunately I don't know how David made the pretty pictures. Is it worth swapping the two solutions, since the washers one is so much easier?
My instincts say yes but it might be a question best left for a 101 instructor, perhaps they drive the shell method into their brains like crazy and so that will be the first choice for students regardless of the difficulty. However, if they cover both methods equally then I would definitely vote this one first, power rule integrals always beat integration by parts in my books.