Multiple integral

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acquistare plaquenil Calculus

acquistare lipitor Fundamental theorem

acheter trental Limits of functions
Continuity

comprar prednisone sin receta Mean value theorem
Rolle’s theorem

compra coversyl Differential

compra xanax Definitions

acheter avelox Derivative (generalizations)

acquistare tulasi Differential

comprar levothroid sin receta infinitesimal
of a function
total

Concepts

Differentiation notation
Second derivative
Third derivative
Change of variables
Implicit differentiation
Related rates
Taylor’s theorem

Rules and identities

Sum
Product
Chain
Power
Quotient
General Leibniz
Faà di Bruno’s formula

Integral

Lists of integrals

Definitions

Antiderivative
Integral (improper)
Riemann integral
Lebesgue integration
Contour integration

Integration by

Parts
Discs
Cylindrical shells
Substitution (trigonometric)
Partial fractions
Order
Reduction formulae

Series

Geometric (arithmetico-geometric)
Harmonic
Alternating
Power
Binomial
Taylor

Convergence tests

Summand limit (term test)
Ratio
Root
Integral
Direct comparison

Limit comparison
Alternating series
Cauchy condensation
Dirichlet
Abel

Vector

Gradient
Divergence
Curl
Laplacian
Directional derivative
Identities

Theorems

Divergence
Gradient
Green’s
Kelvin–Stokes

Multivariable

Formalisms

Matrix
Tensor
Exterior
Geometric

Definitions

Partial derivative
Multiple integral
Line integral
Surface integral
Volume integral
Jacobian
Hessian matrix

Specialized

Fractional
Malliavin
Stochastic
Variations

v
t
e

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.

The multiple integral is a generalization of the definite integral to functions of more than one real variable, for example, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in R2 are called double integrals, and integrals of a function of three variables over a region of R3 are called triple integrals.[1]

Contents

1 Introduction
2 Mathematical definition

2.1 Properties
2.2 Particular cases

3 Methods of integration

3.1 Integrating constant functions
3.2 Use of symmetry
3.3 Normal domains on R2

3.3.1 x-axis
3.3.2 y-axis
3.3.3 Example
3.3.4 Normal domains on R3

3.4 Change of variables

3.4.1 Polar coordinates
3.4.2 Cylindrical coordinates
3.4.
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