definiteintegral
形容词
definite: 明确的,确定的
名词
integral: 积分,不可分割的部分
词语辨析
definite和integral都有"明确的"含义,但在数学术语中,definiteintegral指的是一个函数在一定区间上的积分。
词汇扩充
- indefinite integral: 不定积分
- definite integral: 定积分
- integral calculus: 积分学
近义词
- integral
- Riemann integral
反义词
- derivative: 导数
柯林斯词典(Collins Dictionary)
definite: If something is definite, it is clear and specific.
integral: Something that is integral is very important or necessary.
牛津词典(Oxford Dictionary)
definite: Clearly stated or decided; not vague or doubtful.
integral: Necessary to make a whole complete; essential or fundamental.
用法
- The definite integral of a function f(x) from a to b represents the signed area between the function and the x-axis over the interval [a, b].
- The definite integral of a function gives a numerical value.
- The definite integral is denoted by ∫(a to b) f(x) dx.
例句
The definite integral of the function f(x) from 0 to 1 is equal to 5.
She calculated the definite integral to find the area under the curve.
The definite integral of a constant function is equal to the product of the function value and the interval length.
Definite integrals are used to calculate areas, volumes, and other quantities in mathematics and physics.
An indefinite integral represents a family of functions, while a definite integral gives a specific numerical value.
The definite integral is a fundamental concept in calculus.
Students need to understand the concept of definite integrals to solve advanced mathematical problems.
The definite integral of a continuous function exists if the function is bounded on the interval of integration.
Definite integrals can be evaluated using various techniques, such as the fundamental theorem of calculus.
The definite integral of a positive function represents the area above the x-axis, while a negative function represents the area below the x-axis.
The definite integral is a useful tool for finding the accumulated change of a quantity over time.
Definite integrals are often used in physics to calculate work, displacement, and other physical quantities.
The definite integral of a rate function gives the total change of the quantity over a given interval.
Calculating definite integrals requires knowledge of antiderivatives and the limits of integration.
The definite integral of a function can be approximated using numerical methods, such as the trapezoidal rule or Simpson's rule.
She struggled with finding the definite integral of complex functions.
The definite integral of a constant is equal to the product of the constant and the interval length.
Definite integrals can be used to solve optimization problems by finding the maximum or minimum value of a function over a given interval.
The definite integral is a powerful tool for analyzing the behavior of functions and solving mathematical problems.
Understanding the concept of definite integrals is essential for success in calculus and other advanced mathematical courses.