For continuous distributions, replace the point charge sum with an integral: dE = kdq/$r^2$. Three types: (1) Linear $\frac{lambda C}{m}$: dq = lambdadl; (2) Surface (sigma C/$m^2$): dq = sigmadA; (3) Volume (rho C/$m^3$): dq = rhodV. Important results derived by integration: Ring on axis at distance x: E = $\frac{kQx}{x^2 + R^2}$^$\frac{3}{2}$ along axis. Maximum field of ring at x = $\frac{R}{sqrt}$(2). Infinite line charge: E = $\frac{lambda}{2*pi*epsilon_0*r}$ radially. Infinite plane: E = $\frac{sigma}{2*epsilon_0}$ perpendicular to surface. Strategy: identify symmetry to determine which component survives, then integrate only that component.