tích phân

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The Vietnamese word "tích phân" translates to "integral" in English, and it is primarily used in mathematics, particularly in calculus.

Explanation:

1. Definition: "Tích phân" refers to a mathematical concept that represents the area under a curve or the accumulation of quantities. It is a fundamental concept in calculus used to find things like areas, volumes, and other quantities that can be accumulated.

2. Usage Instructions:

   • "Tích phân" is used when discussing calculus problems, especially when you need to calculate the area under a graph or the total accumulation of a function over a specific interval.
   • It can appear in both academic contexts (like schools and universities) and in practical applications (like physics and engineering).

3. Example:

   • If you have a function that describes the speed of a car over time, the "tích phân" of that function over a certain time period will give you the total distance traveled by the car during that time.

4. Advanced Usage:

   • In advanced mathematics, "tích phân" can be classified into different types, such as definite and indefinite integrals. A definite integral has specific limits and calculates the area under a curve between those limits, while an indefinite integral does not have limits and represents a general form of the accumulation of a function.

5. Word Variants:

   • The term can be related to "đạo hàm," which means "derivative." While "đạo hàm" deals with rates of change, "tích phân" focuses on accumulation and total values.

6. Different Meaning:

   • While "tích phân" primarily refers to the mathematical integral, in some contexts, it can metaphorically refer to the idea of accumulation or gathering in broader discussions, such as collecting experiences or knowledge.

7. Synonyms:

   • In a mathematical context, there are no direct synonyms for "tích phân" in Vietnamese, as it is a specific term. However, you might encounter terms like "hàm tích phân" (integral function) in more complex discussions.

Conclusion:

Understanding "tích phân" is crucial for studying calculus and applying mathematical principles in various fields.

Academic

noun

1. integral