A double integral is a mathematical concept used to calculate the volume under a surface defined by a function of two variables, typically denoted as f(x, y) . It extends the idea of a single integral, which finds the area under a curve, to two dimensions. The double integral is represented as \iint_D f(x, y) \, dA , where D is the region over which the integration occurs, and dA represents an infinitesimal area element. To evaluate a double integral, one often uses iterated integrals, which involve performing two successive integrations. This process can be visualized as summing up small volumes over a specified area in the xy -plane. Double integrals are widely used in various fields, including physics, engineering, and economics, to model and analyze phenomena that depend on two variables, such as mass, probability, and fluid flow.