antiderivative

antiderivative的音标为[ˌæntɪˈdɪvɪtɪv]或[ˌeɪntɪˈdɪvɪtɪv]，意思是“反导数”。速记技巧是使用首字母或缩写来记忆这个单词。例如，可以将单词分解为“an”和“tide”两个部分，或者使用缩写“At”来代替“antidevi”等。基本翻译为“反导数”是因为它表示一个函数在某一点的导数的负值，即函数在该点的变化率。在数学中，反导数通常用于解决一些积分问题。

英文词源：

antiderivative，源于拉丁语“anti-”表示“相反”或“相反方向”，加上“derivatus”衍生自“derivare”意为“获取，取得”，因此antiderivative意为“反向取得，反向积分”。

变化形式：

在英语中，antiderivative可以通过添加前缀或后缀进行变化，如indefinite antiderivative（不确定的反向取得），reciprocal antiderivative（反向积分倒数）等。

相关单词：

1. integral：原意是“整体”，在数学中可以指积分，与antiderivative相反。

2. derivative：源于拉丁语“derivatus”，意为“被获取的”，在数学中指由微积分方程得到的函数。

3. integration：意为“整合，积分”，与antiderivative相反。

4. differential：意为“微分”，与antiderivative相关，表示微分的反方向过程。

5. anti-differential：意为“反微分”，是antiderivative的派生词，用于描述反方向的微分运算。

6. anti-derivative：意为“反向衍生”，用于描述反向求导数的过程。

7. anti-integral：意为“反向积分”，用于描述反向积分的运算过程。

8. anti-derivative function：反导数函数，是一种特殊的函数，具有反向导数的性质。

9. anti-differential operator：反微分算子，是一种数学工具，用于处理反方向的微分运算。

10. antiderivative table：反向积分表，是一种数学表格，用于记录反向积分的计算结果和公式。

常用短语：

1. antiderivative of x = x的不定积分

2. antiderivative of a function f(x) = f(x)的原函数

3. indefinite integral = 不定积分

4. indefinite integration = 不定积分的运算

5. integration = 积分

6. definite integral = 定积分

7. definite integration = 定积分的运算

例句：

1. To find the antiderivative of a function, we need to integrate from left to right.

2. The antiderivative of x^2 + 2x + 1 is (x^3)/3 + 2x^2 + x + C.

3. We can use the integration formula to find the antiderivative of a function.

4. The antiderivative of sin(x) is -cos(x) + C.

5. The indefinite integral of x^2 + 2x + 1 is (x + 1)^2 + C.

6. Definite integration is a fundamental mathematical operation that helps us understand the behavior of functions.

7. Definite integration is used in many areas of mathematics and physics, including calculus, differential equations, and optimization problems.

英文小作文：

The importance of integration in mathematics and physics cannot be overstated. It is a fundamental operation that helps us understand the behavior of functions and solve complex problems. From calculus to differential equations to optimization problems, integration plays a crucial role in many areas of mathematics and physics research. Furthermore, it is also used in engineering and other practical applications to help us understand and predict the behavior of systems and processes. Therefore, integration is not just a mathematical concept, but rather a fundamental tool that helps us understand the world around us.