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integral

/ˈɪntɪɡɹəl/ /ˈɪntəɡɹəl/

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noun

积分

A number, the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed.

Examples :

"The integral of xmapsto x^2 on [0,1] is rac{1}{3}."

x映射到x平方在[0,1]上的积分是三分之一。

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Illustration integral - Image 1

Illustration integral - Image 2

noun

积分，定积分。

A definite integral, a limit of sums.

Examples :

"The integral of the students' daily study time represents the total amount of time they spent learning. "

学生们每日学习时间的积分，代表了他们花在学习上的总时间。

Illustration integral - Image 1

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noun

不定积分，积分

Antiderivative

Examples :

"The integral of x^2 is rac{x^3}{3} plus a constant."

x 平方的积分（不定积分）是 ⅓x³ 加上一个常数。

Illustration integral - Image 1

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adjective

必要的，不可或缺的

Constituting a whole together with other parts or factors; not omittable or removable

Examples :

"The student's attendance is integral to their success in the class. "

学生的出勤对他们在课堂上的成功至关重要。

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adjective

整数的，构成整体所必需的

Of, pertaining to, or being an integer.

Examples :

"The recipe calls for an integral number of eggs, not fractions. "

这个食谱要求用整数个鸡蛋，不能用半个或四分之一个。

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adjective

积分的, 完整的

Relating to integration.

Examples :

"The integral part of a successful school project is collaboration among classmates. "

一个成功的学校项目，其完整的组成部分是同学之间的合作.

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Illustration integral - Image 1

adjective

完整的，未受损伤的。

Whole; undamaged.

Examples :

"The antique vase was integral to the family's collection; it had been passed down undamaged for generations. "

这件古董花瓶对这个家族的收藏至关重要，它完好无损地传承了好几代。