How to Use integral in a Sentence

integral

1 of 2 adjective

• She had become an integral part of their lives.
• Martha is an integral part of that in so many ways.
  — Leo Bertucci, Louisville Courier Journal, 9 Oct. 2025
• Dance played an integral role to the film.
  — Diana Lodderhose, Deadline, 16 Feb. 2026
• Death is an integral part of life.
  — John Kominoski, The Conversation, 10 June 2026
• Phones feel integral to our lives.
  — Lani Ngonethong, Twin Cities, 30 Aug. 2025
• But of course, a boycott can be an integral part of a strike.
  — Whizy Kim, refinery29.com, 27 Aug. 2020
• But yeah, music is very much an integral part of the process for me.
  — Nick Vivarelli, Variety, 17 Apr. 2023
• Movies always have been an integral part of his life.
  — Baz Bamigboye, Deadline, 6 Feb. 2026
• Carlos has been an integral part of this team, both on and off the field.
  — Matt Young, Chron, 23 Mar. 2022
• This makes sense and is integral to our story.
  — Abbey White, HollywoodReporter, 27 Oct. 2025
• And yet no one right now is more integral to the survival of our way of life.
  — Andrew Sullivan, Daily Intelligencer, 29 June 2018
• My husband was an integral part of this.
  — Jeanne Phillips, Mercury News, 17 June 2026
• What used to be a slow month for recruiting is now integral to the process.
  — Jon Wilner, Mercury News, 12 June 2026
• The supreme court rules that a mosque is not integral to Islam.
  — Sangeeta Tanwar, Quartz India, 9 Nov. 2019
• In many ways, that film was integral to my career and a jumping off point.
  — Aaron Couch, The Hollywood Reporter, 24 Apr. 2020
• Dak is a very, very integral part of the success of this football team.
  — Calvin Watkins, Dallas News, 16 Oct. 2020
• Camp life is an integral part of hunting, perhaps the very crux of the sport.
  — Susan Casey, Field & Stream, 6 Dec. 2020
• The dark and cold of space are integral to Webb’s infrared work.
  — Justin Bachman, Anchorage Daily News, 24 Dec. 2021
• Hair, says Dej, has always been an integral part of her life.
  — Lauren Valenti, Vogue, 14 Apr. 2018
• Our feedback loop has played an integral role in shaping the brand.
  — Rachel King, Fortune, 4 May 2020
• Durrett’s love of clothes has always been an integral part of her job.
  — Liana Satenstein, Vogue, 30 Nov. 2021
• The mine is an integral part of what Adani calls its pit-to-plug model.
  — Washington Post, 30 May 2017
• More than that, Albrecht plays an integral role on both ends of the court.
  — Steve Reaven, Chicago Tribune, 16 Feb. 2026
• The train and the briefcase play integral parts in the action.
  — Keith Nelson, Men's Health, 8 Aug. 2022
• After all, guns are an integral part of life here and in many places across the nation.
  — Erik Lacitis, The Seattle Times, 20 Nov. 2018
• That said, something more along the lines of an integral or something like that.
  — Steven Strogatz, Quanta Magazine, 19 Apr. 2023
• This movie isn't just a scary story — scary stories are integral to the plot.
  — Marisa Lascala, Good Housekeeping, 20 May 2022
• This integral part of the room wasn't an easy feat to accomplish, though.
  — Elizabeth Gulino, House Beautiful, 30 May 2019
• This is where your data science skills play an integral role.
  — Rachel Wells, Forbes.com, 26 Aug. 2025
• Swim lessons are still mandatory, and days at the pool are an integral part of life for many.
  — Washington Post, 19 Aug. 2021

integral

2 of 2 noun

• The trick is to expand the integral from one to two dimensions.
  — Rhett Allain, WIRED, 14 Mar. 2023
• The most powerful formula in physics starts with a slender S, the symbol for a sort of sum known as an integral.
  — Quanta Magazine, 6 Feb. 2023
• The path integral is more of a physics philosophy than an exact mathematical recipe.
  — Charlie Wood, Wired, 4 July 2021
• Progress, and much needed for a starter integral to Oakland’s hopes of winning the division and going deep into the postseason.
  — Susan Slusser, SFChronicle.com, 15 Aug. 2020
• Democrats have in turn rallied around expanding voting access as both a civil rights issue and one integral to their future political success.
  — Matthew Brown, USA TODAY, 5 Aug. 2021
• The path integral is a way of describing a particle's travels in terms of a quantum superposition of all possible routes.
  — Ahmed Almheiri, Scientific American, 1 Sep. 2022
• The target was the mythical DOZZ formula—but the gulf between it and the path integral seemed vast.
  — Charlie Wood, Wired, 4 July 2021
• No more will innocent citizens cower in fear at the thought of derivatives and integrals, or flash back in horror to the days of terror and confusion in high-school math class.
  — Sean Carroll, Discover Magazine, 20 Nov. 2019
• The target was the mythical DOZZ formula — but the gulf between it and the path integral seemed vast.
  — Quanta Magazine, 17 June 2021
• To tally the possibilities implied by a loop, theorists must turn to a summing operation known as an integral.
  — Quanta Magazine, 20 Aug. 2020
• The procedure for adding up these infinite field configurations with the proper weighting is known as the Feynman path integral.
  — Charlie Wood, Wired, 4 July 2021
• Physicists then take the integral of every possible path an experiment could follow from beginning to end and add those integrals together.
  — Quanta Magazine, 18 Nov. 2016
• This method gave the group a rough estimate of the entire world population without having to resort to complicated calculation methods such as integrals.
  — Manon Bischoff, Scientific American, 2 Oct. 2025
• Instead their paper uses integrals to calculate the high-dimensional volumes directly—a method a bit like looking at the area inside the cube above (but without the visual reference).
  — Emma R. Hasson, Scientific American, 7 Aug. 2025
• Both Croot and Bloom broke the integral into parts and proved that one main term was large and positive, and that all the other terms (which could sometimes be negative) were too small to make a meaningful difference.
  — Quanta Magazine, 9 Mar. 2022
• The idea is that all mathematical results—whether 1 + 1 = 2 or a complicated integral—can derive from a common foundation.
  — Manon Bischoff, Scientific American, 1 Oct. 2024
• The cutoff independent physics, defined by the Euclidean functional integral over the 4-sphere admits only a finite number of instantons.
  — Sean Carroll, Discover Magazine, 29 Aug. 2012
• The work led him to revisit a particularly powerful invariant called the Kontsevich integral, which contains many other knot invariants rolled up inside it.
  — Erica Klarreich, Quanta Magazine, 22 Apr. 2026
• In comparison, prior constructions involve estimating an integral over many variables, while the latest work involves only two variables regardless of the shape’s dimension.
  — Max Springer, Scientific American, 7 Aug. 2024
• Imagine calculating every possible way billions of Lego bricks could fit together – that’s the scale of complexity physicists face when evaluating the configurational integral.
  — Atharva Gosavi, Interesting Engineering, 16 Sep. 2025