What is the difference between: integers and integrals? I keep hearing them used for the same thing.?

Answer 1

One definition of integral is "expressed or expressible as or in terms of integers." It is the adjective form of integer, not the noun form. So you might talk about the integral value.

It's like the difference between number and numeric.

It's a confusing term, and I would avoid it because more often in mathematics, integral is used as a noun to mean "a calculus method of computing the area under a curve."

And then there is the "normal" definition of integral where it means "an essential part of something", such as mathematics is an integral part of a balanced school curiculum.

Answer 2

The integers (from the Latin integer, which means with untouched integrity, whole, entire) are the set of numbers including the whole numbers (0, 1, 2, 3, …) and their negatives (0, −1, −2, −3, …). In non-mathematical terms, they are numbers that can be written without a fractional or decimal component, and fall within the set {… −2, −1, 0, 1, 2, …}. For example, 65, 7, and −756 are integers; 1.6 and 1½ are not integers.

More formally, the integers are the only integral domain whose positive elements are well-ordered, and in which order is preserved by addition. Like the natural numbers, the integers form a countably infinite set. The set of all integers is often denoted by a boldface Z (or blackboard bold , Unicode U+2124), which stands for Zahlen (German for numbers).[1]

In algebraic number theory, these commonly understood integers, embedded in the field of rational numbers, are referred to as rational integers to distinguish them from the more broadly defined algebraic integers.

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Integration is a core concept of advanced mathematics, specifically in the fields of calculus and mathematical analysis. Given a function f(x) of a real variable x and an interval [a,b] of the real line, the integral


is equal to the area of a region in the xy-plane bounded by the graph of f, the x-axis, and the vertical lines x = a and x = b, with areas below the x-axis being subtracted.

The term "integral" may also refer to the notion of antiderivative, a function F whose derivative is the given function f. In this case it is called an indefinite integral, while the integrals discussed in this article are termed definite integrals. Some authors maintain a distinction between antiderivatives and indefinite integrals.

Answer 3

Integrals are whole numbers like 1,2,3,4,5 and their negatives -1,-2,-3,-4,-5.
5.8, 0.6, 1/4, 3/4 are not integers because they are not whole numbers.

65, 7, and −756 are integers; 1.6 and 1½ are not integers.



The integers (from the Latin integer, which means with untouched integrity, whole, entire) are the set of numbers including the whole numbers (0, 1, 2, 3, …) and their negatives (0, −1, −2, −3, …). In non-mathematical terms, they are numbers that can be written without a fractional or decimal component, and fall within the set {… −2, −1, 0, 1, 2, …}.

Integrals are used in calculus. The term "integral" may also refer to the notion of anti derivative, a function F whose derivative is the given function f. In this case it is called an indefinite integral, while the integrals discussed in this article are termed definite integrals. Some authors maintain a distinction between anti derivatives and indefinite integrals.

These are integrals:
http://www.3dsoftware.com/Calculus/img/Integral7.png

Answer 4

An integer is the set of whole numbers (0, 1, 2, 3, 4, 5,...) and the negative counting numbers (-1, -2, -3, -4, -5....)

An integral is a summation of the values of a function. An indefinite integral is the general formula for that summation. A definite integral is the actual value of that function over a given domain.

Answer 5

An integer is the set of whole numbers that have no fractions or decimals (0, ±1, ±2, ±3, ±4, ±5,...).

An integral is a summation of a number of values, it's a branch of Calculus. It's often used to calculate difficult areas.

Answer 6

intergers are part of the number system that includes negative zero and positive numbers....intergrals are terms used in calculus to get the area under the curve....