3 syllables: in, te, grals. Stress on in.
IN-tuh-gruhlz
/ˈɪntəɡɹəlz/
integrals is pronounced IN-tuh-gruhlz (/ˈɪntəɡɹəlz/). It has three syllables (in-te-grals), with the stress on "in". Integrals refers to the plural form of integral, a fundamental concept in mathematics describing quantities whose sum is determined by accumulation, such as area, probability, or total change. In everyday math usage, it also denotes multiple integral operators or a family of antiderivatives. The term carries formal, technical connotations and appears in advanced calculus contexts, physics, and engineering literature.
Integrals refers to the plural form of integral, a fundamental concept in mathematics describing quantities whose sum is determined by accumulation, such as area, probability, or total change. In everyday math usage, it also denotes multiple integral operators or a family of antiderivatives. The term carries formal, technical connotations and appears in advanced calculus contexts, physics, and engineering literature.
"The integrals of the function f(x) over the interval [a, b] were computed numerically."
"She solved several definite integrals for her advanced calculus homework."
"In physics, integrals describe accumulated quantities like probability and charge distributions."
Pronounce as in-ˈte-grəlz. Primary stress on the second syllable. Break it into three syllables: in-TE-grals, with the final -s making a voiced z sound. IPA: US/UK/AU: ɪnˈtɛɡrəlz (approx) but more precisely /ˈɪn.tə.ɡrəlz/ for US and /ˈɪn.tɪ.ɡ.rəlz/; ensure the first syllable is reduced to a lax ‘ih’ and the middle syllable carries the main stress. Listening reference: Pronounce settings on major dictionaries.
Common errors: 1) Stress on the first syllable (IN-te-grals) instead of second (in-TE-grals). 2) Vowel reduction in the first syllable (ih-N), leading to a dull unstressed sound; aim for a light, unstressed 'in' as /ɪn/. 3) Slurring the middle consonant cluster ‘gr’ with a silent or weak vowel; keep a clear /ɡr/ onset between syllables. Correct by practicing slow: /ˈɪn.tə.ɡrəlz/ and then speed up while preserving the middle vowel quality.
US tends to a rhotacized, slightly shorter middle vowel, with /ˈɪn.tə.ɡrəlz/. UK and AU maintain /ˈɪn.tə.ɡ.rəlz/ with a more pronounced /ɡ/ and clear syllable boundaries; AU may have slightly broader vowel quality in the second syllable and a less pronounced final z. Overall, the rhoticity difference is minor in British and Australian speech, but US often has a more compact, faster rhythm. Listen for the middle /t/ release and the final /z/ sound.
It's challenging because of its multisyllabic structure with three consecutive syllables, a mid-lexical /t/ release, and the final /əlz/ cluster that can blur to /əlz/ or /rəls/ if rushed. The tongue must transition smoothly from the alveolar stop /t/ to the alveolar /r/ and then to a light /əl/ before the /z/. Practicing slow, precise transitions helps stabilize the rhythm and prevents vowel reduction in the middle syllable.
There are no silent letters in integrals, but the primary stress is on the second syllable (in-TE-grals). The letters clearly map to syllables: /ˈɪn.tə.ɡrəlz/. Focus on maintaining stress on syllable two and ensuring the /ɡ/ onset of the third syllable is audible. The -s at the end is voiced, so don’t skip it.
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Integral derives from late Latin integralis, from integrare “to make whole, restore, complete.” The mathematical sense emerges in the 17th century as part of the development of calculus by Newton and Leibniz, where integrals act as the reverse process of differentiation, accumulating infinitesimal quantities. The plural integrals reflects multiple operators or multiple functions’ accumulations. The term aligns with other “integral” roots meaning whole, complete, or complete sum, with the modern sense crystallizing in the 1700s as mathematicians formalized definite and indefinite integrals, antiderivatives, and area-under-curve interpretations. First known uses appear in Renaissance math texts that discuss summing infinitesimals, later becoming central in the work of Euler, Cauchy, and Riemann, who refined notation, convergence, and geometric interpretations. The word carried strong formal mathematics connotations and remains a core concept in calculus, physics, and engineering. Over time, “integrals” expanded to higher dimensions (double, triple, multiple integrals) and to probabilistic metrics, maintaining its root in “whole” or “total.”
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Words that rhyme with "integrals"
-als sounds
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