[미적분] 미분과 적분의 관계에 대한 (relationship between integration and differen…
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[미적분] 미분과 적분의 관계에 대한 (relationship between integration and differentiation)
미적분,미분,적분,calculus,시험,시험자료,전문자료
미분과 적분의 관계에 대한 영어
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…(省略)
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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
다.