In calculus, the inverse of differentiation where smaller and smaller rectangles are squeezed together under a graphed curve, yielding an approximation of the area under the curve.


A less than successful governmental policy of forcing individuals from different ethnic and racial backgrounds to relate to one another under duress. Usually reserved for the youngest and most vulnerable members of a given society.


In psychiatry/psychology, the process of blending together the alternate identities (alters) of an individual with Dissociative Identity Disorder (i.e., Multiple Personality Disorder or MPD). May happen spontaneously or through participation in various forms of psychotherapy. Insofar as alters most often represent differing historical and developmental perspectives on traumatic incidents and the participants in those events, integration is similar to putting into one room with the task of solving a common problem:

Both mothers-in-law
Goths and Young Republicans…
Southern virginal nuns and bawdy earth mothers with belly rings...
Jocks and Geeks
The part of you that wants to do whatever (desperately!) and the part that knows better and is going to tell Mom on you…
Those who think they are cool and those how know they are not…
Children and Grownups (no contest but the grownups are better at rationalization and control the money)…
The kids who are glad the drunken abusive loser father is getting the hell out and the ones clinging desperately to his pants leg…
Deadheads and everybody else…

The most difficult part of integration is achieving accuracy and congruency of real-time perception after years of compartmentalizing every positive and negative emotion and reaction to life. After years of living pretty much one emotion at a time, she/he is learning the everyday pain of ambivalence.

Yes, sometimes she yells at you, but this one will never hit you. Yes, your boyfriend doesn’t always pay attention to you and disappoints you, but because he’s human, not because he thinks you’re less than a piece of shit. Yes, sometimes your girlfriend/boyfriend tries to kiss you and sneak a hand under your shirt, but it’s because they love you and touching you makes them feel closer to Heaven, not as a preamble to raping you. Yes, you can say no and this one will stop.

If you know someone who’s in the process of integrating, hold them (when you can). Tell them you will be there for them. Do a lot of praying. And try and take care of yourself. Try to remember that the same iron determination that got them through their personal hell will get them through this, too.

For L.

Integration in the information technology is the taking of off the shelf (usually brand name) software, commodity hardware and a few scripts to solve an information technology need in a client.

An example of integration might be the design, building and rollout of an accounts receivable system running Oracle on VMS on Dell hardware. The integrators won't call it this, of course, they'll call it ``an enterprise ready fully integrated enterprise management system.'' They will also neglect to train any non-management-level staff in using the software so when the the system is delivered it will not be used by the rank-and-file employees, thus ensuring it never contains the information the managers look for.

In business-speak, integration means the expansion of an enterprise's operations within its existing area of activity via merger or takeover.

Comes in two flavours: horizontal integration - taking over other companies that produce the same goods or services (e.g. a brewery takes over another brewery to increase its market share), and vertical integration - taking over companies active upstream or downstream in the supply chain, their suppliers or distributors (e.g. a brewery takes over a pub chain or a supplier of malt to reduce costs, guarantee supplies or sales, or hinder competitors). Both forms of integration carry the risk that a monopoly may develop.

Here's a first year calculus student's (my) guide to integration.

Integration is a way of finding the area between the x-axis and a curve (or line) on a graph. According to my maths teacher, it works by dividing the area up into an infinite number of infinitesimally small rectangles.

Firstly, let's choose a polynomial to integrate:

x3 + 6x2 + 3x + 8

We also choose a limit, which is how much we want to integrate, we'll choose to integrate the area under the curve between x = 0 and x = 4.

For each term in the equation, we raise the exponent by one and divide that term by the new exponent.

x3 becomes (x4) / 4
6x2 becomes (6x3) / 3, which is the same as 2x3.
3x becomes (3x2) / 2, because 3x is the same as 3x1.
8 becomes 8x, because 8 is the same as 8x0 so it becomes (8x1) / 1 which is 8x.

We use a funky looking ∫ thing to show that it's an integral, apparently it's an Old English S and stands for 'sum'. Our integral is:

   |   x3 + 6x2 + 3x + 8 dx
 0 |

           x4              3x2
    =     ---  +  2x3  +  ----  +  8x
           4                2

We then plug the upper and lower limits into our integral.

4: 44 / 4 + 2 * 43 + 3 * 42 / 2 + 8 * 4 = 248

0: 04 / 4 + 2 * 03 + 3 * 02 / 2 + 8 * 0 = 0

We then take the difference between these two values, so (248 - 0) = 248. The area under the graph where x is between 0 and 4 is 248.

This was a simple polynomial example. You should know that there are some things that cannot be integrated using this technique. See integrating sin(ln(x)) and impossible integral.

A simple mechanics example:

A train starts from rest and accelerates for 5 seconds. While it is accelerating, its velocity in ms-1 is given by the equation v = t2. Find out how far it's travelled after the first 5 seconds.

(Okay, this is pretty unrealistic, a train wouldn't accelerate like that, but just humour me.)

In a velocity-time graph, the area under the graph is always displacement (how far it's travelled), so we integrate to find the area under the graph, which will give us the distance travelled.

Our graph would look something like this...


|                '
|              .
|            '
|         .//|
|         ///|
|      '/////|
0            5              t
The shaded area is the area that we're trying to find. Alright, our equation is:

v = t2

t2 becomes (t3)/3

So our integral is:

   |     t2 dx
 0 |

    =   ---

So we plug in our values.

5: 53 / 3 = 41.666

0: 03 / 3 = 0

Then find the difference to get the area. (41.666 - 0) = 41.666.

ms-1 is just the same as "meters per second", so our answer will be in meters. So the train has travelled 41.7m.

And now you know.

In modern television advertising parlance, Integration is both the act of including product placements in television shows and how effectively that inclusion is handled.

Product integration is a tricky thing to do right - on the one hand, a company wants their brand to be included in a program in such a way as to be noticable to the viewer, but on the other they shouldn't be so incredibly obvious as to lower the viewer's opinion of the brand. In other words, a police car manufactured by Ford is a perfectly reasonable occurrance in your typical Friday night cop show, but a ten-second vanity shot of the Ford logo that brings the plot to a standstill for its duration is a waste of time and money - viewers would remember the brand, sure enough, but their opinion of it would be substantially lowered.

It should be noted that the term Integration doesn't apply to product occurrences outside the normal world of the programming - an on-screen graphic inviting viewers to download episodes of a show from iTunes doesn't fall under integration, but a character saying that she downloaded a kickass song from iTunes does.

In`te*gra"tion (?), n. [L. integratio a renewing, restoring: cf. F. int'egration.]


The act or process of making whole or entire.

2. Math.

The operation of finding the primitive function which has a given function for its differential coefficient. See Integral.

⇒ The symbol of integration is summa sum), and the integral is also regarded as the limiting value of the sum of great numbers of differentials, when the magnitude of the differentials decreases, and their number increases indefinitely. See Limit, n. When the summation is made between specified values of the variable, the result is a definite integral, and those values of the variable are the limits of the integral. When the summation is made successively for two or more variables, the result is a multiple integral.


In the theory of evolution: The process by which the manifold is compacted into the relatively simple and permanent. It is supposed to alternate with differentiation as an agent in development.


© Webster 1913.

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