\int_x^{x^2}\frac{dt}{t^2+3}=-\int_a ^{x} \frac{dt}{t^2+3}+\int_a^{x^2}\frac{dt}{t^2+3}\\Differentiate and apply first fundamental theorem of calculus: \int_x^{x^2}\frac{dt}{t^2+3}=-\frac{d}{dx}\int_a ^{x} \frac{dt}{t^2+3}+\frac{d}{dx}\int_...
FTC(Fundamental Theorem of Calculus)是微积分学中的一个重要定理,有两个版本:FTC Part I和FTC Part II。 FTC Part I: 如果f是一个连续的函数,那么函数F(x)=∫f(t)dt从a到x的值就是f(x)的积分。 FTC Part II: 如果f是一个连续的函数,那么函数F(x)=∫f(t)dt从a到x的反函数f(x)就是f(t)...
FTC1微积分是指第一基本定理（Fundamental Theorem of Calculus，简称FTC）的第一部分，它描述了微积分中的导数和积分之间的关系。FTC1微积分可以帮助我们更好地理解微积分的本质，它告诉我们如何利用导数求出函数的积分或用积分求出函数的导数。FTC1微积分是微积分中的重要概念，它在数学、物理、工程等...
Section 4.3:Fundamental Theorem of Calculus and the Indefinite Integral Essentials Fundamental Theorem of Calculus • The basic mechanism for evaluating a definite integral is the Fundamental Theorem of Calculus (FTC), formally stated as Theorem 4.3.1. Theorem 4.3.1: Fundamental Theor...
FTC- Fundamental Theorem of Calculus Théorème fondamental du calcul Académique et scientifique/Mathématiques FTC- Finance and Trade Centre Centre des finances et du commerce Entreprise/Commerce international FTC- Frente de Trabajadores Cristianos ...
FTCAt the last time,we've learned the First Part of the Fundamental Theorem of Calculus.It shows how indefinite integration and definite integration are related.In the other words,it shows how anti-derivative and the area are related.Today,you'll deeply understand the First FTC by using it....
This note addresses evaluation of Lebesgue integrals on the real line using the Fundamental Theorem of Calculus, without having to verify that the primitive is absolutely continuous.doi:info:doi/10.4169/amer.math.monthly.121.04.361J. J. Koliha...
doi:10.4169/amer.math.monthly.121.04.361This note addresses evaluation of Lebesgue integrals on the real line using the Fundamental Theorem of Calculus, without having to verify that the primitive is absolutely continuous.J. J. KolihaThe University of MelbourneThe American Mathematical Monthly...