What is the definition of a definite integral?
Definition of definite integral : the difference between the values of the integral of a given function f(x) for an upper value b and a lower value a of the independent variable x.
What is the formula for an integral?
Formula for Integration: \int e^x \;dx = e^x+C.
What are the properties of definite integrals?
Properties of Definite Integrals
| Properties | Description |
|---|---|
| Property 1 | ∫kj f(x)dx = ∫kj f(t)dt |
| Property 2 | ∫kj f(x)g(x)=-∫kj f(x)g(x),Also,∫jk f(x)g(x) = 0 |
| Property 3 | ∫kj f(x)g(x)=-∫lj f(x)g(x),Also,∫kl f(x)g(x) = 0 |
| Property 4 | ∫kj f(x)g(x)=∫kj f(j+k-x)g(x) |
What are definite integrals used for?
Definite integrals can be used to determine the mass of an object if its density function is known. Work can also be calculated from integrating a force function, or when counteracting the force of gravity, as in a pumping problem.
What is integration of DX?
The “dx” indicates that we are integrating the function with respect to the “x” variable. In a function with multiple variables (such as x,y, and z), we can only integrate with respect to one variable and having “dx” or “dy” would show that we are integrating with respect to the “x” and “y” variables respectively.
What is definite and indefinite?
The definite article (the) is used before a noun to indicate that the identity of the noun is known to the reader. The indefinite article (a, an) is used before a noun that is general or when its identity is not known. There are certain situations in which a noun takes no article.
Why is it called indefinite integral?
An indefinite integral, sometimes called an antiderivative, of a function f(x), denoted byis a function the derivative of which is f(x). Because the derivative of a constant is zero, the indefinite integral is not unique. The process of finding an indefinite integral is called integration.
What is a definite and indefinite integral?
A definite integral represents a number when the lower and upper limits are constants. The indefinite integral represents a family of functions whose derivatives are f. The difference between any two functions in the family is a constant.