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CHAPTER 6. BASIC INTEGRATION. 6.1 First Indefinite Integrals (Antiderivatives). In this section we introduce antiderivatives, which are exactly what the name implies. These are also called indefinite . Nonetheless, they are necessary to learn for a reasonably complete understanding of standard calculus, and we begin
www.mathportal.org. Integration Formulas. 1. Common Integrals. Indefinite Integral. Method of substitution. ( ( )) ( ). ( ). f g x g xdx f udu. ?. = ?. ?. Integration by parts. ( ) ( ). ( ) ( ). ( ) ( ). f x g x dx f x g x. g x f x dx. ?. ?. = ?. ?. ?. Integrals of Rational and Irrational Functions. 1. 1 n n x x dx. C n. +. = +. +. ?. 1 ln dx x C x. = +.
7.2. 7.3. 7.4. 7.5. CHAPTER 8. 8.1. 8.2. 8.3. 8.4. 8.5. Contents. The Chain Rule. Derivatives by the Chain Rule. Implicit Differentiation and Related Rates. Inverse Functions and Their Derivatives. Inverses of Trigonometric Functions. Integrals. The Idea of the Integral. 177. Antiderivatives. 182. Summation vs. Integration. 187.
In this Chapter, we shall confine ourselves to the study of indefinite and definite integrals and their elementary properties including some techniques of integration. 7.2 Integration as an Inverse Process of Differentiation. Integration is the inverse process of differentiation. Instead of differentiating a function, we are given the
Chapter 3. Integration. 3.1 Indefinite Integration. Integration is the reverse of differentiation. Consider a function f(x) and suppose that there exists another function F(x) such that. dF dx. = f(x). (3.1). For example, if f(x) = 2x, then F(x) = x2 satisfies Eq. (3.1.1). But note that, for example, F(x) = x2 + 1 also satisfies Eq. (3.1.1).
Integration. ¦Ґ лшс э ятп ?. Up to now we have been concerned with extracting information about how a function changes from the function itself. Given knowledge about an 148 Chapter 7 Integration at each, by supposing .. The symbol ? is called an integral sign, and the whole expression is read as “the integral of f(t)
Chapter VII.. on Series, is entirely new. In theIntegral Calculus, immediately after the integration of standard forms, Chapter XXI. has been added, containing simple applicationsof integration. In both the Differential and Integral Calculus, examples illustrat- ing applications to Mechanics and Physics will be found,especially.
4.2.2 Implicit Differentiation. A method of finding the derivative of an implicit function by taking the derivative of each term with respect to the independent variable while keeping the derivative of the dependent variable with respect to the independent variable in symbolic form and then solving for that derivative. If. ),( yxfy. =.
CHAPTER 7 TECHNIQUES OF INTEGRATION. 7.1 Integration by Parts. (page 287). Integration by parts aims to exchange a difficult problem for a possibly longer but probably easier one. It is up to you to make the problem .. F d x requires us to complete 22 - z2 (watch the minus sign):. This is 1 - u2 with u = x - 1 and z = 1 +
2010 Brooks/Cole, Cengage Learning. 371. C H A P T E R 4. Integration. Section 4.1 Antiderivatives and Indefinite Integration. 1. (. ) 3. 4. 3. 4. 2. 6. 2. 6 d d. C x. C x dx x dx x. ?. ?. ?. ?. ?. +. = +. = ?. = ?. ?. ?. ?. 2. 4. 4. 1. 3. 2. 3. 2. 1. 1. 2. 2. 2. 2. 1. 1. 8. 8. 2. 2 d d x. C x x. C dx x dx x x x x. ?. ?. ?. ?. ?. ?. ?. +. = ?. +. ?. ?. ?.
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