计算∫∫x²/y²dxdy,其中D是由曲线x=2,y=x,xy=1所围成

∫∫_D x²/y² dxdy
= ∫(x = 1→2) x² dx ∫(y = 1/x→x) 1/y² dy
= ∫(x = 1→2) x² * (- 1/y) |(y = 1/x→x) dx
= ∫(x = 1→2) - x² * (1/x - x) dx
= ∫(x = 1→2) (x³ - x) dx
= (x⁴/4 - x²/2) |(x = 1→2)
= (16/4 - 4/2) - (1/4 - 1/2)
= 9/4
满意请采纳,谢谢☆∧_∧☆