## Integral

bounded by the graph of ƒ , the x -axis, and the vertical lines x = a and x = b . The term **integral** may also refer to the notion of antiderivative , a function F whose derivative is the given function ƒ . In this case, it is called an indefinite **integral** and is written:

**wikipedia.org**| 2011/9/17 7:29:19

## J integral

The J- **integral** represents a way to calculate the strain energy release rate , or work ( energy ) per unit fracture surface area, in a material. [ 1 ] The theoretical concept of J **integral** was developed in 1967 by Cherepanov [ 2 ] and in 1968 by Jim Rice [ 3 ] independently, who showed

**wikipedia.org**| 2011/8/1 2:14:52

## B Integral

In nonlinear optics , B **Integral** is a measure of the nonlinear phase shift of light. It calculates the exponential growth of the least stable spatial frequency in a laser beam , and is the numerical equivalent of the nonlinear phase shift along the laser system's optical axis. In a multipass

**wikipedia.org**| 2011/2/25 17:46:57

## Multiple integral

The multiple **integral** is a type of definite **integral** extended to functions of more than one real variable , for example, ƒ ( x , y ) or ƒ ( x , y , z ). Integrals of a function of two variables over a region in ℝ 2 are called double integrals. Contents 1 Introduction

**wikipedia.org**| 2011/9/8 18:04:12

## Riemann integral

In the branch of mathematics known as real analysis , the Riemann **integral** , created by Bernhard Riemann , was the first rigorous definition of the **integral** of a function on an interval . [ 1 ] While the Riemann **integral** is unsuitable for many theoretical purposes, it is one of the easiest

**wikipedia.org**| 2011/9/18 9:38:28

## Dirichlet integral

In mathematics , there are several integrals known as the Dirichlet **integral** , after the German mathematician Peter Gustav Lejeune Dirichlet . One of those is This can be derived from attempts to evaluate a double improper **integral** two different ways. It can also be derived using differentiation

**wikipedia.org**| 2011/6/30 6:34:05

## Gaussian integral

The Gaussian **integral** , also known as the Euler-Poisson **integral** or Poisson **integral** , [ 1 ] is the **integral** of the Gaussian function e − x 2 over the entire real line. It is named after the German mathematician and physicist Carl Friedrich Gauss . The **integral** is: This **integral**

**wikipedia.org**| 2011/8/8 12:43:32

## Integral domain

In abstract algebra , an **integral** domain is a commutative ring that has no zero divisors , [ 1 ] and which is not the trivial ring {0}. It is usually assumed that commutative rings and **integral** domains have a multiplicative identity even though this is not always included in the definition

**wikipedia.org**| 2011/7/7 4:22:14

## Differentiation under the integral sign

continuous derivatives for . Then for : This formula is the general form of the Leibniz **integral** rule and can be derived using the fundamental theorem of calculus . The fundamental theorem of calculus is just a particular case of the above formula, for , a constant, and . If both

**wikipedia.org**| 2011/8/18 1:59:28