x=2与y=x的交点坐标是(2,2)
y=x与xy=1在第一象限的交点坐标是(1,1)
xy=1
y=1/x
∴∫(1->2)dx∫(1/x->x)y^2/x^2dy
=∫(1->2)dx*1/x^2 * y^3/3|(1/x->x)
=∫(1->2)dx*1/x^2*(x^3/3-1/3x^3)
=∫(1->2)xdx/3-1/3∫(1->2)dx/x^5
=x^2/6 |(1->2)-1/3*(-1/4)*1/x^4|(1->2)
=1/6(2^2-1^2)+1/12(1/2^4-1/1^4)
=3/6 +1/12 *(1/16-1)
=1/2+1/12*(-15/16)
=1/2-15/192
=(96-15)/192
=81/192
=27/64