Many physically important spatial integrals, such as those needed for finding electric or magnetic fields, can be calculated by a simple method based on elementary geometry, without the need to use the techniques of the calculus or advanced theorems (such as Gauss’s or Ampere’s laws). The method is practically useful, can provide physical insights, and is suitable for mathematically unsophisticated students in introductory courses. We explain this method by applying it to calculate the electric fields due to a uniformly charged plane, line, and spherical surface.