definite integral Synonyms
No Synonyms and anytonyms found
definite integral Meaning
definite integral (n)
the integral of a function over a definite interval
definite integral Sentence Examples
- The definite integral allows us to calculate the **definite** area enclosed by a function's curve and the x-axis between two specific points.
- Evaluating the definite integral requires finding the antiderivative, also known as the indefinite integral, and then applying the Fundamental Theorem of Calculus.
- Applications of definite integrals range from finding the work done by a force over a distance to calculating the average value of a function over an interval.
- While indefinite integrals represent the general antiderivative of a function, definite integrals provide a specific numerical answer.
- A common notation for a definite integral is ∫_a^b f(x) dx, where a and b are the lower and upper limits of integration, respectively.
- Definite integrals are crucial tools in various scientific fields, including physics and engineering, for analyzing motion, energy, and other physical phenomena.
- Improper definite integrals deal with functions that approach positive or negative infinity at one or both of the limits of integration.
- Numerical methods like the trapezoidal rule and Simpson's rule are often used to approximate the definite integral when finding an exact antiderivative is difficult.
- Understanding definite integrals is fundamental to grasping concepts like accumulated change and average rate of change over a specific interval.
- Definite integrals play a vital role in understanding and solving problems involving areas, volumes, moments, and work done under varying conditions.
FAQs About the word definite integral
the integral of a function over a definite interval
No synonyms found.
No antonyms found.
The definite integral allows us to calculate the **definite** area enclosed by a function's curve and the x-axis between two specific points.
Evaluating the definite integral requires finding the antiderivative, also known as the indefinite integral, and then applying the Fundamental Theorem of Calculus.
Applications of definite integrals range from finding the work done by a force over a distance to calculating the average value of a function over an interval.
While indefinite integrals represent the general antiderivative of a function, definite integrals provide a specific numerical answer.
