http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/defintdirectory/DefInt.html
Where you refer to a particular integral I will assume you mean a definite integral. To illustrate why there is no constant of integration in the result of a definite integral let me take a simple example. Consider the definite integral of 1 from 0 to 1. The antiderivative of this function is x + C, where C is the so-called constant of integration. Now to evaluate the definite integral we calculate the difference between the value of the antiderivative at the upper limit of integration and the value of it at the lower limit of integration: (1 + C) - (0 + C) = 1 The C's cancel out. Furthermore, they will cancel out no matter what the either antiderivatives happen to be or what the limits of integration happen to be.
We need more information. Is there a limit or integral? The theorem states that the deivitive of an integral of a function is the function
Application of definitApplication of definite Integral in the real life
yes
An indefinite integral is a version of an integral that, unlike a definite integral, returns an expression instead of a number. The general form of a definite integral is: ∫ba f(x) dx. The general form of an indefinite integral is: ∫ f(x) dx. An example of a definite integral is: ∫20 x2 dx. An example of an indefinite integral is: ∫ x2 dx In the definite case, the answer is 23/3 - 03/3 = 8/3. In the indefinite case, the answer is x3/3 + C, where C is an arbitrary constant.
gemetrically the definite integral gives the area under the curve of the integrand. explain the corresponding interpretation for a line integral.
This makes it possible to give a precise formal definition of both the derivative, and the definite integral - which are both extremely useful concepts in math, physics, and engineering.
Same as any other function - but in the case of a definite integral, you can take advantage of the periodicity. For example, assuming that a certain function has a period of pi, and the value of the definite integral from zero to pi is 2, then the integral from zero to 2 x pi is 4.
What are the Applications of definite integrals in the real life?
If the values of the function are all positive, then the integral IS the area under the curve.
"integral" is primarily an adjective, but in calculus it is usually a noun, as in "the definite integral of a function."
It is a way to approximate a definite integral using trapezoids.