For continuous distributions, replace the point charge sum with an integral: dE = kdq/r^2. Three types: (1) Linear (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 = kQx/(x^2 + R^2)^(3/2) along axis. Maximum field of ring at x = R/sqrt(2). Infinite line charge: E = lambda/(2piepsilon_0r) radially. Infinite plane: E = sigma/(2epsilon_0) perpendicular to surface. Strategy: identify symmetry to determine which component survives, then integrate only that component.