设D是由x2+y2≤1,x≥0,y≥0所围区域,已知∫∫Df(x,y)dσ=π,则∫∫D[f(x,y)+2]dσ=____.
(3/2)π。解析:∫∫D[f(x,y)+2]dσ=∫∫Df(x,y)dσ+2∫∫Ddσ=π+2×(D的面积)=π+π/2=(3/2)π.
设D是由x2+y2≤1,x≥0,y≥0所围区域,已知∫∫Df(x,y)dσ=π,则∫∫D[f(x,y)+2]dσ=____.
(3/2)π。解析:∫∫D[f(x,y)+2]dσ=∫∫Df(x,y)dσ+2∫∫Ddσ=π+2×(D的面积)=π+π/2=(3/2)π.