For example:

x^2 + y^2 + z^2 <= R^2

z >= 0

Can someone help me find the x,y, and z boundaries? Would x and y be -R and R? And would z be 0 and R^2 - x^2 -y^2?

Also, for:

x^2 + y^2 <= R^2 and 0<= z <= H

I'm confused on the boundaries for this one as well. Anyone?

Last one;

If the question only says that a cub with edge length a, what would be the x,y,z boundaries for the triple integral?