Multiple integral

Generalization of definite integrals to functions of multiple variables Integral as area between two curves. Double integral as volume under a surface z = 10 − (⁠x2 − y2/8⁠). The rectangular region at the bottom of the body is the domain of integration, while the surface is the graph of the two-variable function to be integrated. Part of a series of articles aboutCalculus ∫ a b f ′ ( t ) d t = f ( b ) − f ( a ) {\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)} Fundamental theorem Limits Continuity Rolle's theorem Mean value theorem Inverse function theorem Differential Definitions Derivative (generalizations) Differential infinitesimal of a function total Concepts Differentiation notation Second derivative Implicit differentiation Logarithmic differentiation Related rates Taylor's theorem Rules and identities Sum Product Chain Power Quotient L'Hôpital's rule Inverse General Leibniz Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann integral Lebesgue integration Contour integration Integral of inverse functions Nonelementary integral Integration by Parts Discs Cyli