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- DictionaryIn·te·gral/ˈin(t)əɡrəl/
adjective
- 1. necessary to make a whole complete; essential or fundamental: "games are an integral part of the school's curriculum"
- 2. of or denoted by an integer.
noun
- 1. a function of which a given function is the derivative, i.e. which yields that function when differentiated, and which may express the area under the curve of a graph of the function.
The meaning of INTEGRAL is essential to completeness : constituent. How to use integral in a sentence.
Calculus. In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, [a] the other being differentiation.
We can approximate integrals using Riemann sums, and we define definite integrals using limits of Riemann sums. The fundamental theorem of calculus ties integrals and derivatives together and can be used to evaluate various definite integrals.
May 28, 2023 · The Definition of the Definite Integral. In this section we give a definition of the definite integral \(\displaystyle \int_a^b f(x)\,d{x}\) generalising the machinery we used in Example 1.1.1. But first some terminology and a couple of remarks to better motivate the definition.
The basic idea of Integral calculus is finding the area under a curve. To find it exactly, we can divide the area into infinite rectangles of infinitely small width and sum their areas—calculus is great for working with infinite things!
State the definition of the definite integral. Explain the terms integrand, limits of integration, and variable of integration. Explain when a function is integrable.
Learn integral calculus—indefinite integrals, Riemann sums, definite integrals, application problems, and more.
