integration
Business
The act of taking separate parts and combining them to make a whole.
The relevant internal psychological process that is associated with a purchase decision
Calculus
the operation of finding the region in the
the operation of finding the region in the
the operation of finding the region in the
the operation of finding the region in the xy plane bound by the function
Examples of integration in the following topics:

Improper Integrals
 An Improper integral is the limit of a definite integral as an endpoint of the integral interval approaches either a real number or $\infty$ or $\infty$.
 Such an integral is often written symbolically just like a standard definite integral, perhaps with infinity as a limit of integration.
 It is often necessary to use improper integrals in order to compute a value for integrals which may not exist in the conventional sense (as a Riemann integral, for instance) because of a singularity in the function, or an infinite endpoint of the domain of integration.
 However, the Riemann integral can often be extended by continuity, by defining the improper integral instead as a limit:
 Evaluate improper integrals with infinite limits of integration and infinite discontinuity

Iterated Integrals
 An iterated integral is the result of applying integrals to a function of more than one variable.
 An iterated integral is the result of applying integrals to a function of more than one variable (for example $f(x,y)$ or $f(x,y,z)$) in such a way that each of the integrals considers some of the variables as given constants.
 If this is done, the result is the iterated integral:
 Similarly for the second integral, we would introduce a "constant" function of $x$, because we have integrated with respect to $y$.
 Use iterated integrals to integrate a function with more than one variable

Line Integrals
 A line integral is an integral where the function to be integrated is evaluated along a curve.
 A line integral (sometimes called a path integral, contour integral, or curve integral) is an integral where the function to be integrated is evaluated along a curve.
 The function to be integrated may be a scalar field or a vector field.
 This weighting distinguishes the line integral from simpler integrals defined on intervals.
 The line integral finds the work done on an object moving through an electric or gravitational field, for example.

Double Integrals Over Rectangles
 The multiple integral is a type of definite integral extended to functions of more than one real variable—for example, $f(x, y)$ or $f(x, y, z)$.
 Formulating the double integral , we first evaluate the inner integral with respect to $x$:
 We could have computed the double integral starting from the integration over $y$.
 Double integral as volume under a surface $z = x^2 − y^2$.
 The rectangular region at the bottom of the body is the domain of integration, while the surface is the graph of the twovariable function to be integrated.

Change of Variables
 One makes a change of variables to rewrite the integral in a more "comfortable" region, which can be described in simpler formulae.
 The limits of integration are often not easily interchangeable (without normality or with complex formulae to integrate).
 One makes a change of variables to rewrite the integral in a more "comfortable" region, which can be described in simpler formulae.
 When changing integration variables, however, make sure that the integral domain also changes accordingly.
 Use a change a variables to rewrite an integral in a more familiar region

Integration Using Tables and Computers
 Tables of known integrals or computer programs are commonly used for integration.
 Integration is the basic operation in integral calculus.
 We also may have to resort to computers to perform an integral.
 A compilation of a list of integrals and techniques of integral calculus was published by the German mathematician Meyer Hirsch as early as in 1810.
 Computers may be used for integration in two primary ways.

Numerical Integration
 Numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral.
 This article focuses on calculation of definite integrals.
 The basic problem considered by numerical integration is to compute an approximate solution to a definite integral:
 If $f(x)$ is a smooth wellbehaved function, integrated over a small number of dimensions and the limits of integration are bounded, there are many methods of approximating the integral with arbitrary precision.
 There are several reasons for carrying out numerical integration.

Integrative Psychotherapy
 In contrast, integrative psychotherapy attends to the relationship between theory and technique.
 In contrast, an integrative therapist is curious about the "why and how" as well.
 There are many approaches to integrating psychotherapeutic techniques.
 Theoretical integration: This approach requires integrating theoretical concepts from different approaches.
 Assimilative integration: This mode of integration favors a firm grounding in any one system of psychotherapy, but with a willingness to incorporate or assimilate, perspectives or practices from other schools.

Numerical Integration
 Numerical integration is a method of approximating the value of a definite integral.
 These integrals are termed "definite integrals."
 Numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral.
 Numerical integration methods can generally be described as combining evaluations of the integrand to get an approximation to the integral.
 The integrand is evaluated at a finite set of points called integration points and a weighted sum of these values is used to approximate the integral.

Volumes
 Volumes of complicated shapes can be calculated using integral calculus if a formula exists for the shape's boundary.
 A volume integral is a triple integral of the constant function $1$, which gives the volume of the region $D$.
 Using the triple integral given above, the volume is equal to:
 Triple integral of a constant function $1$ over the shaded region gives the volume.
 Calculate the volume of a shape by using the triple integral of the constant function 1