integral

Meanings

• noun

  A mathematical concept representing the summation of the values of a function over a given interval.

  - "The integral of the function f(x) = x^2 from 0 to 2 is equal to 2."
  - "The definite integral of the function f(x) from a to b is the limit of the Riemann sums as the width of the subintervals approaches zero."

---

Pronunciation

1. /ˈɪntɪɡɹəl/
   
   
   
   Source: "https://commons.wikimedia.org/w/index.php?curid=877468"

---

Antonyms

derivative

---

Synonyms

antiderivative , indefinite integral , ∫ , immanent , inherent , necessary

---

Rhymes

Words rhyming with integral
sequel , reheel , feel , real

---

Variants

List of all variants of integral that leads to same result
integral , integralities , integrality , integrally , integrals , integral calculi , integral calculus , integral calculuses , integral domain , integral domains , definite integral , definite integrals , improper integral , improper integrals , indefinite integral , indefinite integrals , Riemann integral , Riemann integrals

---

Etymology

origin and the way in which meanings have changed throughout history.

From the Latin word 'integralis', meaning whole or complete.

---

Trivia

Any details, considerations, events or pieces of information regarding the word

1. The symbol for the integral sign, ∫, is also known as Sigma, after the Greek letter Sigma, which represents sum.

2. The term 'integral' was first used in the English language in the late 15th century to refer to the idea of completeness or wholeness.

---

Related Concepts

informations on related concepts or terms closely associated with the word. Discuss semantic fields or domains that the word belongs to

1. Integration: The inverse operation of differentiation, used to find the antiderivative or indefinite integral of a function.

2. Riemann Sum: A sum used to approximate the definite integral of a function.

3. Fundamental Theorem of Calculus: A theorem that establishes the relationship between differentiation and integration.

---

Quotes

Quotes by authors and personalities

1. Sitting out on the grass … watching the freight trains roll by on the levee at two in the morning, drinking a beer and listening to the music drifting out of the club, is an "integral" part of the whole experience.

   - Tom Piazza,{it}Why New Orleans Matters{/it},2005

2. Stuffed with peanut butter, celery is the quintessential after-school snack; diced, it provides an essential crunch to chicken and potato salads; buttered up, it is an "integral" part of Thanksgiving stuffing.

   - Sara Dickerman,{it}New York Times Magazine{/it},3 Sept. 2006

3. I do know that shoot-'em-ups (and saw-'em-ups) are likely to remain part of our lives, and that suggests a depressing idea: Maybe the love of violence is an "integral" part of human nature …

   - Stephen King,{it}Entertainment Weekly{/it},12 Oct. 2007

---

Culture

Any cultural, historical, or symbolic significance of the word. Explore how the word has been used in literature, art, music, or other forms of expression.

Integrals have been used extensively in various fields of mathematics, physics, and engineering to find areas, volumes, and center of mass. They have also been used to model real-world phenomena such as the motion of objects under the influence of gravity or the behavior of electrical circuits.

How to Memorize "integral"

1. visualize
   

   - Imagine a function as a curve, and the integral as the area under the curve.
   - Visualize the Riemann sum as a series of rectangles that approximate the area under the curve.

2. associate
   

   - Associate the integral symbol ∫ with the word 'sum'.
   - Associate the definite integral with the idea of finding the exact area under a curve.

3. mnemonics
   

   - Use the mnemonic 'Integrate = Int-egr-ate' to remember the definition of integration.
   - Use the mnemonic 'Area under the curve' to remember the meaning of the definite integral.

---

Memorize "integral" using Dictozo

The best and recommended way to memorize integral is, by using Dictozo. Just save the word in Dictozo extension and let the app handle the rest. It enhances the memorization process in two ways:

1. Highlighting:

   Whenever users encounters the saved word on a webpage, Dictozo highlights it, drawing the user's attention and reinforcing memorization.
2. Periodic Reminders:

   Dictozo will send you periodic reminders to remind you the saved word, it will ask you quiz. These reminders could be in the form of notifications or emails, prompting users to recall and reinforce their knowledge.