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integral

adjective

/ˈɪntɪɡr(ə)l/

IPA:

Dictionary definition of integral

Necessary or essential to the completion or functioning of a whole.
"His role in the team was integral to its success."

Detailed meaning of integral

The term is used to describe something that is an indispensable part of a system, entity, or process. An integral part of a machine, for instance, is a component that is necessary for the machine to operate properly. In a similar way, an integral aspect of a company's success is a factor that is necessary for the company to achieve its goals. To be integral means to be essential and necessary to the completion of a whole, making it complete and whole.

In calculus, "integral" refers to the inverse process of differentiation. Given a differentiable function, the derivative of that function represents the rate of change of the function at a given point. The integral, on the other hand, represents the accumulation of this rate of change over a given interval. In mathematical terms, if "f" is a function and "F" is its derivative, then the integral of "f" over a given interval is equal to the function "F" plus a constant. In other words, the integral of a function gives information about the original function that is not captured by its derivative.

Example sentences containing integral

1. Trust and commitment are integral for a successful marriage.
2. The missing piece was integral to the completion of the puzzle.
3. Integral calculus is used to solve problems involving rates of change.
4. The company's culture is integral to its success.
5. The color blue is an integral part of the painting.
6. The process of photosynthesis is integral to the survival of plants.

History and etymology of integral

The adjective 'integral' has its etymological roots in Latin. It is derived from the Latin word 'integralis,' which comes from 'integer,' meaning 'whole' or 'complete.' In Latin, 'integralis' described something that was essential to the completeness or wholeness of a larger entity. As the term made its way into the English language, it retained this sense of being necessary or essential to the completion or functioning of a whole. 'Integral' emphasizes the idea that certain components or elements are indispensable and are an integral part of a larger system, concept, or structure, reflecting its Latin origins in the concept of wholeness and completeness.

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Further usage examples of integral

1. The support from her family was integral to her recovery.
2. The concept of diversity is integral to the company's values.
3. The use of technology is integral to modern society.
4. The study of history is integral to understanding the present.
5. The ability to communicate effectively is an integral part of leadership.
6. The understanding of different perspectives is integral to making informed decisions.
7. Effective communication is integral to fostering understanding and resolving conflicts in relationships.
8. Collaborative teamwork is integral for achieving synergy and delivering successful projects.
9. The integrity of individuals is integral to building and maintaining trust within organizations.
10. Access to quality education is integral to the personal and intellectual development of individuals.
11. In the digital age, technology has become integral to nearly every aspect of our daily lives.
12. Water is an integral resource, essential for the survival and well-being of all living organisms.
13. Integrity and ethical conduct are integral values that guide decision-making in responsible businesses.
14. Mutual respect is integral to building inclusive and harmonious communities.
15. Innovation is integral to driving progress and staying competitive in a rapidly changing world.
16. During difficult times, the support of family and friends can be integral to one's resilience.
17. Creative collaboration is integral to producing groundbreaking works of art and literature.
18. Effective time management is integral for achieving personal and professional goals.
19. Adaptability is integral for individuals and organizations to thrive in an evolving environment.
20. Empathy is an integral quality that fosters compassion and understanding among people.
21. Embracing diversity is integral to creating vibrant and inclusive workplaces.
22. Patience is integral when facing adversity, as it allows for measured and thoughtful responses.
23. Conservation efforts are integral to preserving biodiversity and protecting the planet.
24. Rigorous research is integral to advancing scientific knowledge and making breakthroughs.
25. Transparency in government and organizations is integral for accountability and trust.
26. Love is an integral and profound emotion that enriches the human experience.