∫D∫xydxdy
=∫(1,2)xdx∫(1/x,x)ydy
=∫(1,2)x(x^2-1/x^2)/2dx
=(1/2)∫(1,2)(x^3-1/x)dx
=(1/2)(x^4/4-lnx)|(1,2)
=(1/2)(4-1/4-ln2)