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Calculate the integral: meaning, definitions and examples

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calculate the integral

[ ˈɪntɪɡrəl ]

Verb

^{Context #1 | Verb}

mathematics

To determine the integral of a function, which involves finding the antiderivative of the function. Integrals are used to calculate areas, volumes, and various other quantities in mathematics.

Synonyms

compute the integral, find the antiderivative.

Which Synonym Should You Choose?

Word	Description / Examples
calculate the integral	This phrase is commonly used in formal mathematical or academic settings when you are asked to determine the integral of a function. Please calculate the integral of the given function. In the exam, you will need to calculate the integral of various polynomial functions.
find the antiderivative	This phrase is specifically used when referring to finding the original function whose derivative is the given function. It’s often used in more theoretical or educational contexts. Find the antiderivative of the function f(x) = 3x^2. In this exercise, you need to find the antiderivative of the provided expression.
compute the integral	This phrase is often used interchangeably with 'calculate the integral,' but may imply a more systematic or algorithmic approach, often found in contexts involving computer-assisted calculations. You can use a computer to compute the integral numerically. The software can quickly compute the integral for complex functions.

Word

Description / Examples

calculate the integral

This phrase is commonly used in formal mathematical or academic settings when you are asked to determine the integral of a function.

Please calculate the integral of the given function.
In the exam, you will need to calculate the integral of various polynomial functions.

find the antiderivative

This phrase is specifically used when referring to finding the original function whose derivative is the given function. It’s often used in more theoretical or educational contexts.

Find the antiderivative of the function f(x) = 3x^2.
In this exercise, you need to find the antiderivative of the provided expression.

compute the integral

This phrase is often used interchangeably with 'calculate the integral,' but may imply a more systematic or algorithmic approach, often found in contexts involving computer-assisted calculations.

You can use a computer to compute the integral numerically.
The software can quickly compute the integral for complex functions.

Examples of usage

The students were asked to calculate the integral of the given function.
She spent hours trying to calculate the integral of the complex equation.

Translations

Translations of the word "calculate the integral" in other languages:

🇵🇹 calcular a integral

🇮🇳 इंटीग्रल निकालें

🇩🇪 das Integral berechnen

🇮🇩 hitung integral

🇺🇦 обчислити інтеграл

🇵🇱 obliczyć całkę

🇯🇵 積分を計算する

🇫🇷 calculer l'intégrale

🇪🇸 calcular la integral

🇹🇷 integrali hesapla

🇰🇷 적분을 계산하다

🇸🇦 احسب التكامل

🇨🇿 vypočítat integrál

🇸🇰 vypočítať integrál

🇨🇳 计算积分

🇸🇮 izračunati integral

🇮🇸 reikna heilduna

🇰🇿 интегралды есептеу

🇬🇪 ინტეგრალის გამოთვლა

🇦🇿 inteqralı hesabla

🇲🇽 calcular la integral

Etymology

The term 'integral' in mathematics originated from the Latin word 'integralis', meaning 'whole' or 'complete'. The concept of integration was developed in the 17th century by mathematicians like Isaac Newton and Gottfried Wilhelm Leibniz, and it has since become a fundamental tool in calculus and various fields of mathematics.