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10th Edition

Soo T. Tan

Publisher: Brooks Cole

ISBN: 9781285464640

Chapter 6.5, Problem 43E

Textbook Problem

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In Exercises 35-44, find the average value of the function *f* over the indicated interval [*a*, *b*].

**43.** *f*(*x*) =

To determine

The average value of the given function *f* over the indicated interval
[ a , b ]
.

**Given information:**

The given function is
*f* is integrable in the interval

**Formula used:**

(1) The average value of function *f* over
*f* is integrable on

**Calculation:**

Rewrite the given equation as,

Use integration by substitution and substitute as,

Differentiate both sides of the above expression,

Use formula (1) of average value function, substitute 0 for *a*, 2 for *b*, *u* for
*f*

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

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In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - In Exercises 1-28, evaluate the definite integral....Ch. 6.5 - 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In Exercises 81-86, determine whether the...Ch. 6.5 - In Exercises 81-86, determine whether the...Ch. 6.5 - In Exercises 1-4, use Property 5 of the definite...Ch. 6.5 - In Exercises 1-4, use Property 5 of the definite...Ch. 6.5 - In Exercises 1-4, use Property 5 of the definite...Ch. 6.5 - In Exercises 1-4, use Property 5 of the definite...Ch. 6.5 - Crop YIELD If left untreated on bean stems, aphids...Ch. 6.5 - Absorption OF Drugs Jane took 100 mg of a drug in...Ch. 6.5 - Absorption OF DRUGS The concentration of a drug in...Ch. 6.6 - Suppose f and g are continuous functions such that...Ch. 6.6 - Write an expression in terms of definite integrals...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 1-8, find the area of the shaded...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 9-16, sketch the graph, and find the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 17-26, sketch the graph of the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 27-34, sketch graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - In Exercises 3542, sketch the graph, and find the...Ch. 6.6 - Effect of Advertising on Revenue In the...Ch. 6.6 - Pulse Rate During Exercise In the accompanying...Ch. 6.6 - Oil Production Shortfall Energy experts disagree...Ch. 6.6 - Air Purification To study the effectiveness of air...Ch. 6.6 - Motion of Two Cars Two cars start out side by side...Ch. 6.6 - Comparison of companies revenues The rate of...Ch. 6.6 - Mexicos hedging Tactic Agustin Carstens, the...Ch. 6.6 - Turbo-charged engine versus standard Engine In...Ch. 6.6 - Alternative Energy Sources Because of the...Ch. 6.6 - Effect of TV advertising on car Sales Carl...Ch. 6.6 - Population Growth In an endeavor to curb...Ch. 6.6 - British Deficit The projected public spending by...Ch. 6.6 - In Exercises 5558, determine whether the statement...Ch. 6.6 - The area of the region bounded by the graphs of...Ch. 6.6 - In Exercises 5558, determine whether the statement...Ch. 6.6 - In Exercises 5558, determine whether the statement...Ch. 6.6 - Show that the area of a region R bounded above by...Ch. 6.6 - In Exercises 1-6, (a) plot the graphs of the...Ch. 6.6 - In Exercises 1-6, (a) plot the graphs of the...Ch. 6.6 - In Exercises 1-6, (a) plot the graphs of the...Ch. 6.6 - In Exercises 1-6, (a) plot the graphs of the...Ch. 6.6 - In Exercises 1-6, (a) plot the graphs of the...Ch. 6.6 - In Exercises 1-6, (a) plot the graphs of the...Ch. 6.6 - In Exercises 7-12, (a) plot the graphs of the...Ch. 6.6 - In Exercises 7-12, (a) plot the graphs of the...Ch. 6.6 - In Exercises 7-12, (a) plot the graphs of the...Ch. 6.6 - In Exercises 7-12, (a) plot the graphs of the...Ch. 6.6 - In Exercises 7-12, (a) plot the graphs of the...Ch. 6.6 - In Exercises 7-12, (a) plot the graphs of the...Ch. 6.6 - Refer to Example 1. Find the area of the larger...Ch. 6.7 - a. Define consumers surplus. Give a formula for...Ch. 6.7 - a. Define the accumulated (future) value of an...Ch. 6.7 - Define the amount of an annuity. Give a formula...Ch. 6.7 - Explain the following terms, (a) Lorenz curve and...Ch. 6.7 - Consumers surplus The demand function for a...Ch. 6.7 - Consumers Surplus The demand function for a...Ch. 6.7 - Consumers Surplus It is known that the quantity...Ch. 6.7 - Producers Surplus The supplier of the portable...Ch. 6.7 - Producers Surplus The supply function for the CDs...Ch. 6.7 - Consumers Surplus The demand function for a...Ch. 6.7 - Producers Surplus The manufacturer of the brand of...Ch. 6.7 - Consumers Surplus The demand function for a...Ch. 6.7 - Producers Surplus The manufacturer of the Blu-ray...Ch. 6.7 - Consumers and producers Surplus The management of...Ch. 6.7 - Consumers and Producers Surplus The quantity...Ch. 6.7 - Refer to Example 3, page 486. Verify that...Ch. 6.7 - Future value of an Investment The newly opened...Ch. 6.7 - Future Value of an Investment An investment is...Ch. 6.7 - Present Value of an Investment Suppose an...Ch. 6.7 - Franchises Camille purchased a 15-year franchise...Ch. 6.7 - The amount of an Annuity Find the amount of an...Ch. 6.7 - The Amount of an Annuity Find the amount of an...Ch. 6.7 - Value of an Investment An investment generates a...Ch. 6.7 - Business Decisions Sharon, the owner of the...Ch. 6.7 - The Amount of an Annuity Aiso deposits 150/month...Ch. 6.7 - Custodial Accounts The Armstrongs wish to...Ch. 6.7 - Present value of an Annuity Estimate the present...Ch. 6.7 - Present Value of an Annuity Estimate the present...Ch. 6.7 - Lottery Payments A state lottery commission pays...Ch. 6.7 - Reverse Annuity Mortgages Sinclair wishes to...Ch. 6.7 - Reverse Annuity Mortgage Refer to Exercise 27....Ch. 6.7 - Gini Index The income distribution of a certain...Ch. 6.7 - Gini Index A certain countrys income distribution...Ch. 6.7 - Lorenz Curves A certain countrys income...Ch. 6.7 - Lorenz Curves A certain countrys income...Ch. 6.7 - Lorenz curves In a study conducted by a certain...Ch. 6.7 - Lorenz Curves In a study conducted by a certain...Ch. 6.7 - Re-solve Example 1, Section 6.7, using a graphing...Ch. 6.7 - Re-solve Exercise 11, Section 6.7, using a...Ch. 6.7 - The demand function for a certain brand of travel...Ch. 6.7 - Investment A is expected to generate income at the...Ch. 6.7 - Investment A is expected to generate income at the...Ch. 6 - Fill in the blanks. 1. a. A function F is an...Ch. 6 - Fill in the blanks. 2. a. cf(x)dx= b....Ch. 6 - Fill in the blanks. 3. a. A differential equation...Ch. 6 - Fill in the blanks. 4. If we let u = g(x), then du...Ch. 6 - Fill in the blanks. 5. a. If f is continuous and...Ch. 6 - Fill in the blanks. 6. a. The Fundamental Theorem...Ch. 6 - Fill in the blanks. 7. a. If f is continuous on...Ch. 6 - Fill in the blanks. 8. If f and g are continuous...Ch. 6 - Fill in the blanks. 9. a. The consumers surplus is...Ch. 6 - Fill in the blanks. 10. a. The accumulated value...Ch. 6 - Fill in the blanks. 11. The amount of an annuity...Ch. 6 - Fill in the blanks. 12. The coefficient of...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercises 1-20, find each indefinite integral...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercise 21-32, evaluate each definite...Ch. 6 - In Exercises 33-36, find the function f given that...Ch. 6 - In Exercises 33-36, find the function f given that...Ch. 6 - In Exercises 33-36, find the function f given that...Ch. 6 - In Exercises 33-36, find the function f given that...Ch. 6 - In Exercises 37 and 38, refer to the following...Ch. 6 - In Exercises 37 and 38, refer to the following...Ch. 6 - Let f(x) = 2x2 + 1, and compute die Riemann sum of...Ch. 6 - Growth rue of Smartphone Users The rate of growth...Ch. 6 - Computer Resale Value Franklin National Life...Ch. 6 - Marginal Cost Functions The management of National...Ch. 6 - Marginal Revenue Functions Refer to Exercise 42....Ch. 6 - Measuring Temperature The temperature on a certain...Ch. 6 - DVD Sales The total number of DVDs sold to U.S....Ch. 6 - Air Pollution On an average summer day, the level...Ch. 6 - Marginal Cost Functions The management of a...Ch. 6 - U.S. Census The number of Americans aged 45-54...Ch. 6 - Commuter Trends Because of the increasing cost of...Ch. 6 - Supply: Womens Boots The rate of change of the...Ch. 6 - Online Retail Sales Since the inception of the...Ch. 6 - Projection TV Sales The marketing department of...Ch. 6 - Sales: Loudspeakers Sales of the Acrosonic model F...Ch. 6 - Find the area of the region under the curve y =...Ch. 6 - Find the area of the region under the curve y =...Ch. 6 - Find the area of the region bounded by the graph...Ch. 6 - Find the area of the region bounded by the curve y...Ch. 6 - Find the area of the region that is completely...Ch. 6 - Find the area of the region between the curve y =...Ch. 6 - Oil Production On the basis of current production...Ch. 6 - Find the average value of the function f(x)=xx2+16...Ch. 6 - Average Temperature The temperature (in degrees...Ch. 6 - Average Velocity of A truck A truck traveling...Ch. 6 - Membership in Credit Unions The membership in...Ch. 6 - Demand for Digital Camcorder Tapes The demand...Ch. 6 - Consumers and Producers Surplus The quantity...Ch. 6 - Retirement Account Savings Chi-Tai plans to...Ch. 6 - Installment Contracts Glenda sold her house under...Ch. 6 - Present Value of a Franchise Alicia purchased a...Ch. 6 - Income Distribution OF A Country A certain...Ch. 6 - Population Growth The population of a certain...Ch. 6 - Find (2x3+x+2x2x)dx.Ch. 6 - Find f if f(x) = ex + x and f(0) = 2.Ch. 6 - Find xx2+1dx.Ch. 6 - Evaluate 01x2x2dx.Ch. 6 - Find the area of the region completely enclosed by...

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