积分域 D 的面积 S = ∫ u^2du = 1/3.∫∫ f(u,v)dudv 是常数,设为C,f(x,y)=xy+C,两边在 D 上取重积分,得C =∫∫ xydxdy +CS即 C =∫dx∫ xydy +C/32C/3 = ∫xdx[y^2/2] = ∫x^5/2dx = 1/12,得 C = 1/8,则 f(x,y)=xy...
积分域 D 的面积 S = ∫ u^2du = 1/3.∫∫ f(u,v)dudv 是常数,设为C,f(x,y)=xy+C,两边在 D 上取重积分,得C =∫∫ xydxdy +CS即 C =∫dx∫ xydy +C/32C/3 = ∫xdx[y^2/2] = ∫x^5/2dx = 1/12,得 C = 1/8,则 f(x,y)=xy...