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Chapter 8 - Applications of Definite Integrals

8.1 Accumulation and Net Change
8.2 Areas in the Plane
8.3 Volumes
Chapter 8 Reviews

By this point it should be apparent that finding the limits of Riemann sums is not just an intellectual exercise; it is a natural way to calculate mathematical or physical quantities that appear to be irregular when viewed as a whole, but which can be fragmented into regular pieces.  We calculate values for the regular pieces using known formulas, then sum them to find a value for the irregular whole.  This approach to problem solving was around for thousands of years before calculus came along, but it was tedious work and the more accurate you wanted to be the more tedious it became.

With calculus it became possible to get exact​ answers for these problems with almost no effort, because in the limit these sums became definite integrals and definite integrals could be evaluated with antiderivatives.  With calculus, the challenge became one of finding an antiderivative for it.  In this chapter you will do precisely that, find areas between irregular curves and volumes of irregular solids.  (Taken from an excerpt in the fifth edition of the Finney, Demana, Waits, Kennedy, and Bressoud textbook Calculus - Graphical, Numerical, Algebraic.)

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  • Home
  • Integrated Math 3
    • Homework Calendars
    • Chapter 2 - Linear Equations, Inequalities, and Functions >
      • 2-1/2-2 Solving Equations/Inequalities
      • 2-3 Linear Functions and Slope-Intercept Form
      • 2-4 Families of Functions
      • 2-5 Absolute Value Functions and Graphs
      • 2-6 Two-Variable Inequalities
      • 2-7 Solving Systems of Equations
      • 2-8 Systems of Inequalities
      • 2-9 Systems With Three Variables
      • Chapter 2 Reviews
    • Chapter 3 - Quadratic Functions and Equations >
      • 3-1 Quadratic Functions and Transformations
      • 3-2 Standard Form of a Quadratic Function
      • 3-3 Factoring Quadratic Expressions
      • 3-3b Intercept Form
      • 3-4 Quadratic Equations
      • Graphing Quadratics Handouts
      • 3-5 Completing the Square
      • 3-6 The Quadratic Formula
      • Chapter 3 Reviews
    • Chapter 4 Polynomials and Polynomial Functions >
      • 4-1 Polynomial Functions
      • 4-2 Adding, Subtracting, and Multiplying Polynomials
      • 4-3 Polynomials, Linear Factors, and Zeros
      • 4-4 Solving Polynomial Equations
      • 4-5 Dividing Polynomials
      • 4-6 Theorems About Roots of Polynomial Equations
      • Chapter 4 Handouts
      • Chapter 4 Reviews
    • Chapter 5 - Rational Expressions and Functions >
      • 5-1 Simplifying Rational Expressions
      • 5-2 Multiplying and Dividing Rational Expressions
      • 5-3 Adding and Subtracting Rational Expressions
      • 5-5 The Reciprocal Function Family
      • 5-7 Solving Rational Equations
      • Chapter 5 Handouts
      • Chapter 5 Reviews
    • Chapter 6 - Radical Expressions and Functions >
      • 6-1 Roots and Radical Expressions
      • 6-2 Multiplying and Dividing Radical Expressions
      • 6-3 Binomial Radical Expressions
      • 6-4 Rational Exponents
      • 6-5 Solving Square Root and Other Radical Equations
      • 6-6 Functions Operations
      • 6-7 Inverse Relations and Functions
      • 6-8 Graphing Radical Functions
      • Chapter 6 Handouts
      • Chapter 6 Reviews
    • Chapter 7 - Exponential and Logarithmic Functions >
      • 7-1 Exploring Exponential Models
      • 7-2 Properties of Exponential Functions
      • 7-3 Logarithmic Functions as Inverses
      • 7-4 Properties of Logarithms
      • 7-5 Exponential and Logarithmic Equations
      • 7-6 Natural Logarithms
      • Chapter 7 Handouts
      • Chapter 7 Reviews
    • Chapter 8 - Trigonometric Functions >
      • 8-0 Right Triangle Trigonometry
      • 8-1 Exploring Periodic Data
      • 8-2 Angles and the Unit Circle
      • 8-3 Radian Measure
      • Chapter 8 Handouts
      • Chapter 8 Reviews
    • Spring 2019 Final Project
  • About
  • Contact