Multiple integrals extend the concept of integration to functions of more than one variable. They allow us to calculate quantities like area, volume, and mass over regions in two or three dimensions. For example, a double integral can be used to find the area under a surface in three-dimensional space, while a triple integral can determine the volume of a solid. In mathematical notation, a double integral is expressed as ∫∫ f(x, y) dA, where f(x, y) is a function of two variables, and dA represents an infinitesimal area element. Similarly, a triple integral is written as ∫∫∫ f(x, y, z) dV, with dV representing an infinitesimal volume element. These integrals are essential in fields like physics and engineering for solving problems involving multiple dimensions.