Here's a worked question:
Shouldn't the second to last line be:
$\displaystyle -3 \int^2_0 \int^3_0 \int^1_0 u^2 du dv dw$
where -3 is the Jacobian? Where did the $\displaystyle \frac{1}{3}$ come from?
Haven't done these recently enough to fully check all the steps (without spending a lot of time brushing up), however I can point out that (in the image) the third line up from the bottom has the absolute value of the reciprocal of the expression that came out to -3 above. So the absolute value of the reciprocal of -3 is 1/3. If that's not enough then I'm sure someone else will be able to help you further.