设f(x,y)=xy+f(u,v)dudv,

题目

设f(x,y)=xy+f(u,v)dudv,

如题,

答案

∫∫f(u,v)dudv 是一个数,记为 A,则 f(x,y) = xy+A,两边在D上作二重积分,得∫∫f(x,y)dxdy =∫∫xydxdy + A∫∫dxdy 即 A = ∫∫xydxdy + AσA =∫xdx∫ydy + A∫x^2dx =∫x^5/2dx + A/3,得 2A/3 = 1/12,A=1/8,则 f(...