Important Terms and Concepts

Learning OutcomesIn this chapter, students will...

Chapter 5 Sections
51 Integrals of the Reciprocal Function, a Population Growth Problem
Objective: Work with the problems in this section on your own or with your study group as an assignment after completing chapter 4.
Homework: Problems 16 all
Objective: Work with the problems in this section on your own or with your study group as an assignment after completing chapter 4.
Homework: Problems 16 all
52 Linear Approximations and Differentials
Objective: Given the equation for a function f and a fixed point on its graph, find an equation for the linear function that best fits the given function. Use the equation to find approximate values for f(x) and values for the differentials dx in dy.
Homework: Q Problems 110, Problems 15 odd, 6, 741 odd.
Objective: Given the equation for a function f and a fixed point on its graph, find an equation for the linear function that best fits the given function. Use the equation to find approximate values for f(x) and values for the differentials dx in dy.
Homework: Q Problems 110, Problems 15 odd, 6, 741 odd.
53 Formal Definition of Antiderivative and Indefinite Integral
Objective: Become familiar with the symbol used for an indefinite integral or an antiderivative by using this symbol to evaluate indefinite integrals.
Homework  Day 1: Q Problems 110, Problems 137 odd.
Homework  Day 2: Problems 242 even.
Objective: Become familiar with the symbol used for an indefinite integral or an antiderivative by using this symbol to evaluate indefinite integrals.
Homework  Day 1: Q Problems 110, Problems 137 odd.
Homework  Day 2: Problems 242 even.
54 Riemann Sums and the Definition of Definite Integrals
Objective: Use Riemann sums and limits to define and estimate values of definite integrals
Homework: Q Problems 110, Problems 111 odd.
Objective: Use Riemann sums and limits to define and estimate values of definite integrals
Homework: Q Problems 110, Problems 111 odd.
55 The Mean Value Theorem and Rolle's Theorem
Objective: Learn the mean value theorem and Rolle's theorem and learn how to find the point in an interval at which the instantaneous rate of change of the function equals the average rate of change.
Homework  Day 1: Q Problems 110, Problems 1, 2, 321 odd.
Homework  Day 2: Problems 2333 odd, 34, 3941 all.
Objective: Learn the mean value theorem and Rolle's theorem and learn how to find the point in an interval at which the instantaneous rate of change of the function equals the average rate of change.
Homework  Day 1: Q Problems 110, Problems 1, 2, 321 odd.
Homework  Day 2: Problems 2333 odd, 34, 3941 all.
56 The Fundamental Theorem of Calculus
Objective: Derive the fundamental theorem of calculus, and use it to evaluate definite integrals algebraically.
Homework: Q Problems 110, Problems 1, 710 all
Objective: Derive the fundamental theorem of calculus, and use it to evaluate definite integrals algebraically.
Homework: Q Problems 110, Problems 1, 710 all
57 Definite Integral Properties and Practice
Objective: Be able to evaluate quickly a definite integral, in an acceptable format, using the fundamental theorem of calculus.
Homework  Day 1: Q Problems 110, Problems 123 odd
Homework  Day 2: Problems 2537 odd, 38
Objective: Be able to evaluate quickly a definite integral, in an acceptable format, using the fundamental theorem of calculus.
Homework  Day 1: Q Problems 110, Problems 123 odd
Homework  Day 2: Problems 2537 odd, 38
58 Definite Integrals Applied to Area and Other Problems
Objective: Given a problem in which a quantity varies with , learn a systematic way to write a definite integral for the product of and , and evaluate the interval by using the fundamental theorem.
Homework  Day 1: Q Problems 110, Problems 111 odd
Homework  Day 2: Problems 1331 odd
Objective: Given a problem in which a quantity varies with , learn a systematic way to write a definite integral for the product of and , and evaluate the interval by using the fundamental theorem.
Homework  Day 1: Q Problems 110, Problems 111 odd
Homework  Day 2: Problems 1331 odd
59 Volume of a Solid by Plane Slicing
Objective: Given a solid whose crosssectional area varies along its length, find it’s volume by slicing into slabs and performing appropriate calculus, and show that the answer is reasonable.
Homework  Day 1: Q Problems 110, Problems 14 all
Homework  Day 2: Problems 59 all
Homework  Day 3: Problems 1115 all
Homework  Day 4: Problems 16, 1723 odd
Objective: Given a solid whose crosssectional area varies along its length, find it’s volume by slicing into slabs and performing appropriate calculus, and show that the answer is reasonable.
Homework  Day 1: Q Problems 110, Problems 14 all
Homework  Day 2: Problems 59 all
Homework  Day 3: Problems 1115 all
Homework  Day 4: Problems 16, 1723 odd
510 Definite Integrals Numerically by Graphing Calculator and by Simpson’s Rule
Objective: Use your calculator’s builtin numerical integration feature or Simpson’s rule to find approximate values of definite integrals.
Homework: Q Problems 110, Problems 1, 4, 5, 6, 7, 11, 15, 16
Objective: Use your calculator’s builtin numerical integration feature or Simpson’s rule to find approximate values of definite integrals.
Homework: Q Problems 110, Problems 1, 4, 5, 6, 7, 11, 15, 16