[미적분] 미분과 적분의 관계에 대한 資料 (relationship between integration and differen…
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미분과 적분의 관계에 대한 영어資料
미적분,미분,적분,calculus,시험,시험자료,전문자료
미분과 적분의 관계에 대한 영어자료theorem들과 definition들을 정리해서 보기 좋음.시험 전에 정리하기 위한 자료로 좋음. , [미적분] 미분과 적분의 관계에 대한 자료 (relationship between integration and differentiation)시험자료전문자료 , 미적분 미분 적분 calculus 시험
5. The Relation between Integration and Differentiation.
Theorem 5.1. First Fundamental Theorem of Calculus.
Theorem 5.2. Zero-Derivative Theorem.
Theorem 5.3. Second Fundamental Theorem of Calculus.
5. The Relation between Integration and Differentiation.
Theorem 5.1. First Fundamental Theorem of Calculus. Let f be a function that is integrable on [a,x] for each x in [a,b]. Let c be such that a ≤ c ≤ b and define a new function A as follows:
A(x) = if a ≤ x ≤ b. Then the derivative A`(x) exists at each point x in the open interval (a,b) where f is continuous, and for such x we have A`(x) = f(x).
Theorem 5.2. Zero-Derivative Theorem. If f`(x) = 0 for each x in an open interval I, then f is constant on I.
Definition of Primitive Function. A function P is called a primitive(or an antiderivative) of a function f on an open interval I if the derivative of P is f, that is, if P`(x) = f(x) for all x in I.
- x-δ < t < x+δ, |f(t) - f(x)| < ε/2, .
Theorem 5.3. Second Fundamental Theorem of Calculus. Assume f is continuous on an open interval I, and let P be any primitive of f on I. Then, for each c and each x in I, we have
P(x) = P(c) + .
- A(x) = .
Point. Inte…(drop)
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[미적분] 미분과 적분의 관계에 대한 資料 (relationship between integration and differentiation)
순서
theorem들과 definition들을 요점해서 보기 좋음.
시험 전에 요점하기 위한 資料로 좋음.
다.
