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MAT 1221 survey of Calculus Section 6.1 Antiderivatives and Indefinite Integrals http://myhome.spu.edu/lauw
Expectation Simplify your answers. For problem 2: Formally answer the question in full sentence Pay attention to the units
Preview Introduce antiderivatives/ indefinite integral Introduce integration formulas Initial Value Problems Word Problems
Reverse Operation of Differentiation
Example 1 is the derivative of is an antiderivative of
Example 1 is the derivative of functions of the form
Example 1 The antiderivative of is of the form
Differential Integral Sign
Notation Constant of Integration/ Arbitrary Constant Integrand
Notation The notation always comes in pair.
Example 3 Tradition
Remark on the integral notation Use parenthesis if there are two or more terms in a sum or difference.
Differential Equations and Initial Conditions
Differential Equations and Initial Condition
The antiderivative of the derivative is the original function.
(b) Find the area of the wound after 7 days. The area of the wound after 7 days is cm 2
MTH 252 Integral Calculus Chapter 6 – Integration Section 6.2 – The Indefinite Integral Copyright © 2005 by Ron Wallace, all rights reserved.
Barnett/Ziegler/Byleen Business Calculus 11e1 Learning Objectives for Section 13.1 Antiderivatives and Indefinite Integrals The student will be able to.
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Section 4.3 Indefinite Integrals and Net Change Theorem Math 1231: Single-Variable Calculus.
MAT 1221 Survey of Calculus Section 7.1 Integration by Parts
MAT 1221 Survey of Calculus Section 6.4 Area and the Fundamental Theorem of Calculus
Antiderivatives Definition A function F(x) is called an antiderivative of f(x) if F ′(x) = f (x). Examples: What’s the antiderivative of f(x) = 1/x ?
Formal Definition of Antiderivative and Indefinite Integral Lesson 5-3.
5.c – The Fundamental Theorem of Calculus and Definite Integrals.
MAT 1221 Survey of Calculus Section 2.5 The Chain Rule
MAT 1235 Calculus II 4.1, 4.2 Part I The Definite Integral
INTEGRALS 5. INTEGRALS In Section 5.3, we saw that the second part of the Fundamental Theorem of Calculus (FTC) provides a very powerful method for evaluating.
Section 4.1 – Antiderivatives and Indefinite Integration.
Antiderivatives: Think “undoing” derivatives Since: We say is the “antiderivative of.
MAT 1235 Calculus II 4.5 Part I The Substitution Rule
CHAPTER 6: DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELING SECTION 6.2: ANTIDIFFERENTIATION BY SUBSTITUTION AP CALCULUS AB.
The Indefinite Integral
Antiderivatives Indefinite Integrals. Definition A function F is an antiderivative of f on an interval I if F’(x) = f(x) for all x in I. Example:
4.1 : Anti-derivatives Greg Kelly, Hanford High School, Richland, Washington.
Sect. 4.1 Antiderivatives Sect. 4.2 Area Sect. 4.3 Riemann Sums/Definite Integrals Sect. 4.4 FTC and Average Value Sect. 4.5 Integration by Substitution.
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