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7th Edition

Waner + 1 other

Publisher: Cengage Learning,

ISBN: 9781337291248

Chapter 6.4, Problem 49E

Textbook Problem

In Exercises 45–54, calculate the total area of the region described. Do not count area beneath the x-axis as negative. [**HINT:** See Example 6.]

Bounded by the line
*x*-axis, and the lines

and

Applied Calculus

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[HinT:...Ch. 6.1 - Find f(x) if f(0)=1 and the tangent line at...Ch. 6.1 - Find f(x) if f(1)=1 and the tangent line at...Ch. 6.1 - Find f(x) if f(0)=0 and the tangent line at...Ch. 6.1 - Find f(x) if f(1)=1 and the tangent line at...Ch. 6.1 - Marginal Cost The marginal cost of producing the...Ch. 6.1 - Marginal Cost The marginal cost of producing the...Ch. 6.1 - Marginal Cost The marginal cost of producing the...Ch. 6.1 - Marginal Cost The marginal cost of producing the...Ch. 6.1 - Facebook Membership At the start of 2010, Facebook...Ch. 6.1 - Uploads to YouTube Since YouTube first became...Ch. 6.1 - Median Household Income From 2000 to 2007, median...Ch. 6.1 - Mean Household Income From 2000 to 2007 the mean...Ch. 6.1 - Bottled Water Sales The rate of U.S. sales of...Ch. 6.1 - Bottled Water Sales The rate of U.S. per capita...Ch. 6.1 - Health-Care Spending in the 1990s Write H(t) for...Ch. 6.1 - Health-Care Spending in the 2000s Write H(t) for...Ch. 6.1 - Subprime Mortgage during the Housing Bubble At the...Ch. 6.1 - Subprime Mortgage Debt during the Housing Bubble...Ch. 6.1 - Motion in a Straight Line The velocity of a...Ch. 6.1 - Motion in a Straight Line The velocity of a...Ch. 6.1 - Vertical Motion under Gravity If a stone is...Ch. 6.1 - Vertical Motion under Gravity If a stone is thrown...Ch. 6.1 - Vertical Motion under Gravity Your name is Galileo...Ch. 6.1 - Vertical Motion under Gravity Your name is...Ch. 6.1 - Tailwinds The ground speed of an airliner is...Ch. 6.1 - Headwinds The ground speed of an airliner is...Ch. 6.1 - Vertical Motion Show that if a projectile is...Ch. 6.1 - Vertical Motion Use the result of Exercise 69 to...Ch. 6.1 - Exercises 7176 use the results of Exercises 69 and...Ch. 6.1 - Exercises 7176 use the results of Exercises 69 and...Ch. 6.1 - Exercises 7176 use the results of Exercises 69 and...Ch. 6.1 - Exercises 7176 use the results of Exercises 69 and...Ch. 6.1 - Exercises 7176 use the results of Exercises 69 and...Ch. 6.1 - Exercises 7176 use the results of Exercises 69 and...Ch. 6.1 - Why is this section called The Indefinite...Ch. 6.1 - If the derivative of Julius is Augustus, then...Ch. 6.1 - Linear functions are antiderivatives of what kind...Ch. 6.1 - Constant functions are antiderivatives of what...Ch. 6.1 - If we know the derivative of a function, do we...Ch. 6.1 - If we know an antiderivative of a function, do we...Ch. 6.1 - If F(x) and G(x) are both antiderivatives of f(x),...Ch. 6.1 - Your friend Marco claims that once you have one...Ch. 6.1 - Complete the following: The total cost function is...Ch. 6.1 - Complete the following: The distance covered is an...Ch. 6.1 - If x represents the number of items manufactured...Ch. 6.1 - If t represents time in seconds since liftoff and...Ch. 6.1 - Why was the following marked wrong? 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In Exercises 7784, use Mikes shortcut method (see...Ch. 6.2 - In Exercises 7784, use Mikes shortcut method (see...Ch. 6.2 - In Exercises 7784, use Mikes shortcut method (see...Ch. 6.2 - In Exercises 7784, use Mikes shortcut method (see...Ch. 6.2 - In Exercises 7784, use Mikes shortcut method (see...Ch. 6.2 - Cost The marginal cost of producing the xth roll...Ch. 6.2 - Cost The marginal cost of producing the xth box of...Ch. 6.2 - Economic Growth The Mexico GDP (total monetary...Ch. 6.2 - Housing Starts: The Great Recession The Great...Ch. 6.2 - Revenue: Pacific Sunwear The annual revenue of...Ch. 6.2 - Revenue: Google The annual revenue of Google Inc....Ch. 6.2 - Scientific Research: 19832003 The number of...Ch. 6.2 - Scientific Research: 19832003 The number of...Ch. 6.2 - Sales The rate of sales of your companys Jackson...Ch. 6.2 - Sales The rate of sales of your companys Jackson...Ch. 6.2 - Motion in a Straight Line The velocity of a...Ch. 6.2 - Motion in a Straight Line The velocity of a...Ch. 6.2 - Bottled Water Sales (Compare Exercise 55 in...Ch. 6.2 - Bottled Water Sales (Compare Exercise 56 in...Ch. 6.2 - Are there any circumstances in which you should...Ch. 6.2 - You are asked to calculate uu2+1du. What is wrong...Ch. 6.2 - If the x s do not cancel in a substitution, that...Ch. 6.2 - At what stage of a calculation using a u...Ch. 6.2 - Consider (xx21+3xx2+1)dx. To compute it, you...Ch. 6.2 - If the substitution u=x21 works in xx21dx, why...Ch. 6.2 - Why was the following calculation marked wrong?...Ch. 6.2 - Why was the following calculation marked wrong?...Ch. 6.2 - Why was the following calculation marked wrong?...Ch. 6.2 - Why was the following calculation marked wrong?...Ch. 6.2 - Show that none of the following substitutions work...Ch. 6.2 - Show that none of the following substitutions work...Ch. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 29-34, the graph of the derivative...Ch. 6.3 - In Exercises 29-34, the graph of the derivative...Ch. 6.3 - In Exercises 29-34, the graph of the derivative...Ch. 6.3 - In Exercises 29-34, the graph of the derivative...Ch. 6.3 - In Exercises 29-34, the graph of the derivative...Ch. 6.3 - In Exercises 29-34, the graph of the derivative...Ch. 6.3 - In Exercises 35-38, use technology to approximate...Ch. 6.3 - In Exercises 35-38, use technology to approximate...Ch. 6.3 - In Exercises 35-38, use technology to approximate...Ch. 6.3 - In Exercises 35-38, use technology to approximate...Ch. 6.3 - Pumps A pump is delivering water into a tank at a...Ch. 6.3 - Pumps A pump is delivering water into a tank at a...Ch. 6.3 - Cost The marginal cost function for the...Ch. 6.3 - Cost Repeat Exercise 41 using the marginal cost...Ch. 6.3 - Profit: iPhones Assume that Apples marginal cost...Ch. 6.3 - Profit: PlayStation 4s Assume that Sony's marginal...Ch. 6.3 - Bottled Water Sales The rate of U.S. sales of...Ch. 6.3 - Bottled Water Sales The rate of U.S. per capita...Ch. 6.3 - Online Payments The following graph shows the rate...Ch. 6.3 - Online Auctions The following graph shows the rate...Ch. 6.3 - Scientific Research Exercises 49 and 50 are based...Ch. 6.3 - Scientific Research Exercises 49 and 50 are based...Ch. 6.3 - Graduate Degrees: Women The following graph shows...Ch. 6.3 - Graduate Degrees: Men The following graph how the...Ch. 6.3 - Visiting Students in the Early 2000s The aftermath...Ch. 6.3 - Visiting Students in the Early 2000s Repeat...Ch. 6.3 - Net Income: Exercises 55 and 56 are based on the...Ch. 6.3 - Net Income: Exercises 55 and 56 are based on the...Ch. 6.3 - Crude Oil Production: Mexico The following table...Ch. 6.3 - Offshore Crude Oil Production: Mexico The...Ch. 6.3 - Motion under Gravity The velocity of a tone moving...Ch. 6.3 - Motion under Gravity The velocity of a stone...Ch. 6.3 - Motion A model rocket ha upward velocity...Ch. 6.3 - Motion A race car has a velocity given by...Ch. 6.3 - Facebook Membership From the start of 2007, new...Ch. 6.3 - Uploads to YouTube Since YouTube first became...Ch. 6.3 - Big Brother The total number of wiretaps...Ch. 6.3 - Big Brother The number of wiretaps authorized each...Ch. 6.3 - Surveying My uncle intends to build a...Ch. 6.3 - Pollution An aerial photograph of an ocean oil...Ch. 6.3 - Oil Consumption: United States During the period...Ch. 6.3 - Oil Consumption: China Repeat Exercise 69 using...Ch. 6.3 - The Normal Curve The normal distribution curve,...Ch. 6.3 - The Normal Curve The normal distribution curve,...Ch. 6.3 - If f(x)=6, then the left Riemann sum __________...Ch. 6.3 - If f(x)=1, then the left Riemann sum _________...Ch. 6.3 - If f is an increasing function of x, then the left...Ch. 6.3 - If f is a decreasing function of x, then the left...Ch. 6.3 - If abf(x)dx=0, what can you say about the graph of...Ch. 6.3 - Sketch the graphs of two (different) functions f...Ch. 6.3 - The definite integral counts the area under the...Ch. 6.3 - Sketch the graph of a nonconstant function whose...Ch. 6.3 - Sketch the graph of a nonconstant function whose...Ch. 6.3 - Besides left and right Riemann sums, another...Ch. 6.3 - Your cellphone company charges you c(t)=20t+100...Ch. 6.3 - Your friend's cellphone company charges her...Ch. 6.3 - Give a formula for the right Riemann sum with n...Ch. 6.3 - Refer to Exercise 85. If f is continuous, what...Ch. 6.3 - Sketch the graph of a nonzero function whose left...Ch. 6.3 - When approximating a definite integral by...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. 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[HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - A number of the following exercises are similar to...Ch. 6.4 - A number of the following exercises are similar to...Ch. 6.4 - Cost The marginal cost of producing the xth box of...Ch. 6.4 - Revenue The marginal revenue of the xth box of...Ch. 6.4 - Profit: iPhones (Compare Exercise 43 in Section...Ch. 6.4 - Profit: PlayStation 4s (Compare Exercise 44 in...Ch. 6.4 - Motion A car traveling down a road has a velocity...Ch. 6.4 - Motion A ball thrown in the air has a velocity of...Ch. 6.4 - Motion A car slows to a stop at a stop sign, then...Ch. 6.4 - Motion A truck slows, doesnt quite stop at a stop...Ch. 6.4 - Fuel Consumption The way Professor Waner drives,...Ch. 6.4 - Fuel Consumption The way Professor Costenoble...Ch. 6.4 - Bottled Water Sales (Compare Exercise 45 in...Ch. 6.4 - Bottled Water Sales (Compare Exercise 46 in...Ch. 6.4 - Facebook Membership (Compare Exercise 63 in...Ch. 6.4 - Uploads to YouTube (Compare Exercise 64 in Section...Ch. 6.4 - Big Brother (Compare Exercise 65 in Section 6.3.)...Ch. 6.4 - Big Brother (Compare Exercise 66 in Section 6.3.)...Ch. 6.4 - Economic Growth (Compare Exercise 87 in Section...Ch. 6.4 - Housing Starts: The Great Recession (Compare...Ch. 6.4 - Sales Weekly sales of your Lord of the Rings...Ch. 6.4 - Sales Annual sales of fountain pens in Littleville...Ch. 6.4 - Embryo Development The oxygen consumption of a...Ch. 6.4 - Embryo Development The oxygen consumption of a...Ch. 6.4 - Online Payments The rate of change of total...Ch. 6.4 - Online Auctions The rate of change n(t) of the...Ch. 6.4 - Cost Use the Fundamental Theorem of Calculus to...Ch. 6.4 - Cost The total cost of producing x items is given...Ch. 6.4 - Scientific Research: 19832003 (Compare Exercise 91...Ch. 6.4 - Scientific Research: 19832003 (Compare Exercise 92...Ch. 6.4 - The Logistic Function and High School Graduates a....Ch. 6.4 - The Logistic Function and Grant Spending a. Show...Ch. 6.4 - Kinetic Energy The work done in accelerating an...Ch. 6.4 - Einsteins Energy Equation According to the special...Ch. 6.4 - Explain how the indefinite integral and the...Ch. 6.4 - What is definite about the definite integral?Ch. 6.4 - The total change of a quantity from time a to time...Ch. 6.4 - Complete the following: The total sales from time...Ch. 6.4 - What does the Fundamental Theorem of Calculus...Ch. 6.4 - If Felice and Philipe have different...Ch. 6.4 - Give an example of a nonzero velocity function...Ch. 6.4 - Give an example of a nonzero function whose...Ch. 6.4 - Give an example of decreasing function f(x) with...Ch. 6.4 - Explain why, in computing the total change of a...Ch. 6.4 - If f(x) isa continuous function defined for xa,...Ch. 6.4 - Use the result of Exercises 99 and technology to...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - In Exercises 19 and 20, use the given graph to...Ch. 6 - In Exercises 19 and 20, use the given graph to...Ch. 6 - In Exercises 2126, calculate the left Riemann sum...Ch. 6 - In Exercises 2126, calculate the left Riemann sum...Ch. 6 - In Exercises 2126, calculate the left Riemann sum...Ch. 6 - In Exercises 2126, calculate the left Riemann sum...Ch. 6 - In Exercises 2126, calculate the left Riemann sum...Ch. 6 - In Exercises 2126, calculate the left Riemann sum...Ch. 6 - In Exercises 27 and 28, use technology to...Ch. 6 - In Exercises 27 and 28, use technology to...Ch. 6 - In Exercises 29 and 30, the graph of the...Ch. 6 - In Exercises 29 and 30, the graph of the...Ch. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - In Exercises 4144, find the area of the specified...Ch. 6 - In Exercises 4144, find the area of the specified...Ch. 6 - In Exercises 4144, find the area of the specified...Ch. 6 - In Exercises 4144, find the area of the specified...Ch. 6 - Sales At OHaganBooks.com, the rate of net sales...Ch. 6 - Demand If OHaganBooks.com were to give away its...Ch. 6 - Motion under Gravity Billy-Sean OHagans friend...Ch. 6 - Motion under Gravity An overworked employee at...Ch. 6 - Projected Sales Before OHaganBooks.com launched...Ch. 6 - Bandwidth Billy-Sean OHagan has been using the...Ch. 6 - Sales Sales at the OHaganBooks.com website of...Ch. 6 - Sales The following graph shows the approximate...Ch. 6 - Promotions Unlike sales of Larry Potter and the...Ch. 6 - Sales Even worse than with the leather-bound...Ch. 6 - Website Activity The number of hits on the...Ch. 6 - Website Crashes The latest DoorsXL servers that...Ch. 6 - Student Intern Costs The marginal monthly cost of...Ch. 6 - Legal Costs The legal team maintained by...Ch. 6 - Projected Sales When OHaganBooks.com was about to...Ch. 6 - Actual Sales Once OHaganBooks.com actually went...Ch. 6 - Revised Actual Sales OHaganBooks.com modeled its...Ch. 6 - Computer Usage A consultant recently hired by...Ch. 6 - What (if any) advantages are there to using a...

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