Important Terms and Concepts
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Learning OutcomesIn this chapter, students will...
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Chapter 5 Sections
5-1 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 1-6 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 1-6 all
5-2 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 1-10, Problems 1-5 odd, 6, 7-41 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 1-10, Problems 1-5 odd, 6, 7-41 odd.
5-3 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 1-10, Problems 1-37 odd.
Homework - Day 2: Problems 2-42 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 1-10, Problems 1-37 odd.
Homework - Day 2: Problems 2-42 even.
5-4 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 1-10, Problems 1-11 odd.
Objective: Use Riemann sums and limits to define and estimate values of definite integrals
Homework: Q Problems 1-10, Problems 1-11 odd.
5-5 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 1-10, Problems 1, 2, 3-21 odd.
Homework - Day 2: Problems 23-33 odd, 34, 39-41 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 1-10, Problems 1, 2, 3-21 odd.
Homework - Day 2: Problems 23-33 odd, 34, 39-41 all.
5-6 The Fundamental Theorem of Calculus
Objective: Derive the fundamental theorem of calculus, and use it to evaluate definite integrals algebraically.
Homework: Q Problems 1-10, Problems 1, 7-10 all
Objective: Derive the fundamental theorem of calculus, and use it to evaluate definite integrals algebraically.
Homework: Q Problems 1-10, Problems 1, 7-10 all
5-7 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 1-10, Problems 1-23 odd
Homework - Day 2: Problems 25-37 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 1-10, Problems 1-23 odd
Homework - Day 2: Problems 25-37 odd, 38
5-8 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 1-10, Problems 1-11 odd
Homework - Day 2: Problems 13-31 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 1-10, Problems 1-11 odd
Homework - Day 2: Problems 13-31 odd
5-9 Volume of a Solid by Plane Slicing
Objective: Given a solid whose cross-sectional 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 1-10, Problems 1-4 all
Homework - Day 2: Problems 5-9 all
Homework - Day 3: Problems 11-15 all
Homework - Day 4: Problems 16, 17-23 odd
Objective: Given a solid whose cross-sectional 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 1-10, Problems 1-4 all
Homework - Day 2: Problems 5-9 all
Homework - Day 3: Problems 11-15 all
Homework - Day 4: Problems 16, 17-23 odd
5-10 Definite Integrals Numerically by Graphing Calculator and by Simpson’s Rule
Objective: Use your calculator’s built-in numerical integration feature or Simpson’s rule to find approximate values of definite integrals.
Homework: Q Problems 1-10, Problems 1, 4, 5, 6, 7, 11, 15, 16
Objective: Use your calculator’s built-in numerical integration feature or Simpson’s rule to find approximate values of definite integrals.
Homework: Q Problems 1-10, Problems 1, 4, 5, 6, 7, 11, 15, 16