2 ≤ y ≤ 4
y=4/x ⇒ x=4/y
y=x-1 ⇒ x=y+1
Поэтому:
4/y ≤ x ≤ y+1
Получим:
= ∫ ^(4)_(2)[b]([/b] ∫^(y+1) _(4/y)xdx[b])[/b]dy=
= ∫ ^(4)_(2)[b]([/b](x^2/2)|^(y+1)_(4/y)[b])[/b]dy=
= ∫ ^(4)_(2)[b]([/b] ((y+1)^2/2) -(8/y^2)[b])[/b]dy=
=((y+1)^3/6)+(8/y)|^(4)_(2)=((5^3-3^3)/6)+8*((1/4)-(1/2) ) =(49/3)-2=[b]43/3[/b]