積分

• Reading: せきぶん
• Romaji: sekibun
• Kanji breakdown: 積 (seki) — accumulate, pile up | 分 (bun) — divide, part
• Pronunciation: /se.ki.bɯ.n/

Meaning

Integration; integral calculus. The mathematical operation of finding the integral of a function, used to calculate areas, volumes, and accumulated quantities.

One of the two main operations of calculus alongside 微分 (differentiation). The fundamental theorem of calculus states that differentiation and integration are inverse operations. Key terms: 定積分 (definite integral), 不定積分 (indefinite integral), 積分定数 (constant of integration). Essential in physics for calculating displacement from velocity.

Examples

1. 速度関数を時間で積分することで、ある時間帯における移動距離を求められる。 By integrating the velocity function over time, the distance travelled during a given period can be found.
2. 微分と積分は逆の操作であり、二つを合わせて微積分学と呼ぶ。 Differentiation and integration are inverse operations, and together they are called calculus.
3. 工学では積分を用いて、複雑な曲線で囲まれた面積を正確に計算する。 In engineering, integration is used to accurately calculate the area enclosed by complex curves.

Usage Guide

Context: mathematics, physics, engineering

Tone: technical

Origin & History

Compound of 積 (seki) meaning 'accumulate, pile up' and 分 (bun/fun) meaning 'divide, part'. The metaphor of accumulating infinitely small parts reflects the Riemann sum definition of integration.

Cultural Context

Era: Meiji–Modern

Generation: Students and researchers

Social background: Academic