S:(x-a)^2+y^2+z^2=a^2
则dS=adxdy/[a^2-(x-a)^2-y^2]^(1/2)
∴∫∫(S)(x^2+y^2+z^2)dS
=2∫∫(So)2a^2xdxdy/[a^2-(x-a)^2-y^2]^(1/2) So:(x-a)^2+y^2=a^2
令x=a+rcost,y=rsint 则dxdy=rdrdt
原式=2∫∫(So')2a^2*r*(a+rcost)drdt/(a^2-r^2)^(1/2)
=2*2a^3∫(0,a)rdr/(a^2-r^2)^(1/2)∫(0,2π)dt
=8πa^4 S:(x-a)^2+y^2+z^2=a^2
则dS=adxdy/[a^2-(x-a)^2-y^2]^(1/2)
∴∫∫(S)(x^2+y^2+z^2)dS
=2∫∫(So)2a^2xdxdy/[a^2-(x-a)^2-y^2]^(1/2) So:(x-a)^2+y^2=a^2
令x=a+rcost,y=rsint 则dxdy=rdrdt
原式=2∫∫(So')2a^2*r*(a+rcost)drdt/(a^2-r^2)^(1/2)
=2*2a^3∫(0,a)rdr/(a^2-r^2)^(1/2)∫(0,2π)dt
=8πa^4