∫∫D(x^2+y^2)dδ,其中D={(X,Y)|y=0,x=0,x+y=1}大神快到碗里来

Question

∫∫D(x^2+y^2)dδ,其中D={(X,Y)|y=0,x=0,x+y=1}
大神快到碗里来

Answer 1

原式=∫dx∫(x^2+y^2)dy
=∫[x^2(1-x)+(1-x)^3/3]dx
=∫(1/3-x+2x^2-4x^3/3)dx
=1/3-1/2+2/3-1/3
=1/6.