Multiple Integrals

Multiple integrals are mathematical tools used to calculate the total quantity of something spread out over a region, such as area, volume, or other properties. When dealing with simple shapes, a single integral sums up small parts along one dimension. Multiple integrals extend this idea to two or more dimensions, allowing us to find the total over complex, multi-dimensional regions. For example, they can determine the volume of an irregularly shaped object or the total mass of a region with varying density. They are fundamental in fields like physics, engineering, and applied mathematics for analyzing multidimensional systems.