作变换x=rcosu,y=rsinu,原式=∫<0,π/2>du∫r^2dr+∫<π/2，π>du∫<0,1>r^2dr=∫<0,π/2>[1-(cosu)^3]/3*du+π/6=(1/3)[u-sinu+(1/3)(sinu)^3]|<0,π/2>+π/6=（1/3）[π/2-2/3]+π/6=π/3-2/9.
