help with a couple of questions

[jlmac2001]

1. What is (integral over all space) delta^3(r-r0)r^2d^3r where d^3r=dxdydz=dV and r0=(0,1,2)?

answer: I'm not quite sure what the intergral over all space means.How can r0 be integrated if it's just given as points?

2. Obtain Coulomb's law for the electric field of a point charge from Gauss's law, by considering a spherical surface S of radius r with a point charge +q at its center.

answer: I don't know how to do this. Can someone help? Please!

[HallsofIvy]

Originally posted by jlmac2001
1. What is (integral over all space) delta^3(r-r0)r^2d^3r where d^3r=dxdydz=dV and r0=(0,1,2)?

answer: I'm not quite sure what the intergral over all space means.How can r0 be integrated if it's just given as points?

2. Obtain Coulomb's law for the electric field of a point charge from Gauss's law, by considering a spherical surface S of radius r with a point charge +q at its center.

answer: I don't know how to do this. Can someone help? Please!

1. r0 can't be integrated- its a constant! The integration is over space. delta(r-r0) is DEFINED as having integral, over all space, equal to 1. r0= (0, 1, 2) but that's really not relevant. The integral is still 1. More important would be integral delta^3(r- r0)f(x,y,z) dV= f(0,1,2).