Example M3.
-
Sketch the region defined by the following system of simultaneous inequalities:
$$
x\ge0,\
y\ge0,\
{1\over2}\sqrt{x^2+y^2}\le z\le 3.
$$
-
Suppose the given region contains a charge density $\rho_V$
whose values depend only on distance from the $z$-axis, i.e.,
$\rho_V=\rho_V(\sqrt{x^2+y^2})$ is a function of just one variable.
Express the total charge in the region as a single definite
integral.