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f(x)DX=F(x)+C, ifF(x)=f(x). In this definition, the is called the integral symbol, f(x) is called the integral, x is called the variable of integration, DX is called the differential of the variable x, and C is called the constant of integration.
Basic integration formulas. The fundamental use of integration is as a continuous version of summing. But, paradoxically, often integrals are computed by viewing integration as essentially an inverse operation to differentiation. (That fact is the so-called Fundamental Theorem of Calculus.)
The Simple English Wiktionary has a definition for: integration. Integration may be any of the following: Integration, in the most general sense, may be any bringing together and uniting of things: the integration of two or more economies, cultures, religions (usually called syncretism), etc.
The basic rules of integration, which we will describe below, include the power, constant coefficient (or constant multiplier), sum, and difference rules. We will provide some simple examples to demonstrate how these rules work.
Integration is a way of adding slices to find the whole. Integration can be used to find areas, volumes, central points and many useful things. But it is easiest to start with finding the area under the curve of a function like this: What is the area under y = f(x) ?
Integration occurs when separate people or things are brought together, like the integration of students from all the district's elementary schools at the new middle school, or the integration of snowboarding on all ski slopes. You may know the word differentiate, meaning “set apart.” Integrate is its opposite.
Antiderivative and the Indefinite Integral There is an infinite number of antiderivative of a function f(x), all differing only by a constant C: (F(x)+C)=F(x)+C=f(x)+0=f(x). The set of all antiderivative for a function f(x) is called the indefinite integral of f(x) and is denoted as.
An indefinite integral is a function that takes the antiderivative of another function. It is visually represented as an integral symbol, a function, and then a DX at the end.
There are several steps one must go through in order to properly use the formula: Step 1: Let u = f(x) and DV = g(x) DX, where f(x) g(x) DX is the original integral. Good choices to make are integrals DV = g(x) DX, which are easy to integrate. Step 2: Compute Du = f'(x) DX and v = g(x) DX.
If the value of the integral gets closer and closer to a finite value, the integral is said to converge to that value. If not, the integral is said to diverge. The integral is called an indefinite integral, which represents a class of functions (the antiderivative) whose derivative is the integral.
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