Please help me check if the following reasoning is correct: When considering line and surface integrals, one must integrate over a scalar or vector field. The infinitesimal line (dl) or surface (dA) segments can be treated either as vectors or scalars. Therefore, the only types of line and surface integrals one can run into are: Vector x vector Vector . vector Scalar . vector Scalar . scalar Vector . scalar Volume integrals, on the other hand, are simpler, since the infinitesimal volume segment (dV) can only be treated as a scalar. Therefore, we can only run into the following types of volume integrals: Scalar . scalar Vector . scalar Does this check out? Tell me what you think.