Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 1
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Chapter 7 Applications of Definite Integrals
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 7.1 Integral As Net Change
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 6 What you’ll learn about Linear Motion Revisited General Strategy Consumption Over Time Net Change from Data Work …and why The integral is a tool that can be used to calculate net change and total accumulation.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 7 Example Linear Motion Revisited
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 8 Example Linear Motion Revisited
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 7- 9 Strategy for Modeling with Integrals
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Potato Consumption
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Work
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Hooke’s Law
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example A Bit of Work
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example A Bit of Work
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 7.2 Areas in the Plane
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Review
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide What you’ll learn about Area Between Curves Area Enclosed by Intersecting Curves Boundaries with Changing Functions Integrating with Respect to y Saving Time with Geometric Formulas …and why The techniques of this section allow us to compute areas of complex regions of the plane.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Area Between Curves
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Area Between Curves
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Applying the Definition
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Area of an Enclosed Region
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Integrating with Respect to y
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Integrating with Respect to y
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 7.3 Volumes
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Review
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide What you’ll learn about Volumes As an Integral Square Cross Sections Circular Cross Sections Cylindrical Shells Other Cross Sections …and why The techniques of this section allow us to compute volumes of certain solids in three dimensions.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Volume of a Solid
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide How to Find Volumes by the Method of Slicing
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Square Cross Sections
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Square Cross Sections
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example A Solid of Revolution
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Finding Volumes Using Cylindrical Shells
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Finding Volumes Using Cylindrical Shells
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Finding Volumes Using Cylindrical Shells
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Finding Volumes Using Cylindrical Shells
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Other Cross Sections
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Other Cross Sections
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 7.4 Lengths of Curves
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Review
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide What you’ll learn about A Sine Wave Length of a Smooth Curve Vertical Tangents, Corners, and Cusps …and why The length of a smooth curve can be found using a definite integral.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example The Length of a Sine Wave
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example The Length of a Sine Wave
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Arc Length: Length of a Smooth Curve
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Applying the Definition
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example A Vertical Tangent
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Getting Around a Corner
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide What you’ll learn about Work Revisited Fluid Force and Fluid Pressure Normal Probabilities …and why It is important to see applications of integrals as various accumulation functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Finding the Work Done by a Force
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Work Done Lifting
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Work Done Lifting
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Work Done Lifting
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Fluid Force and Fluid Pressure
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example The Great Molasses Flood if 1919 At 1:00 pm on January 15, 1919, a 90-ft-high, 90-foot-diameter cylindrical metal tank in which the Puritan Distilling Company stored molasses at the corner of Foster and Commercial streets in Boston’s North End exploded. Molasses flooded the streets 30 feet deep, trapping pedestrians and horses, knocking down buildings and oozing into homes. It was eventually tracked all over town and even made its way into the suburbs via trolley cars and people’s shoes. It took weeks to clean up. (a) Given that the tank was full of molasses weighing 100 lb/ft 3, what was the total force exerted by the molasses on the bottom of the tank at the time it ruptured? (b) What was the total force against the bottom foot-wide band of the tank wall?
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example The Great Molasses Flood if 1919
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example The Great Molasses Flood if 1919
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Probability Density Function (pdf)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Normal Probability Density Function (pdf)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide The Rule for Normal Distributions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example A Telephone Help Line Suppose a telephone help line takes a mean of 1.5 minutes to answer a call. If the standard deviation is 0.2, then 68% of the calls are answered in the range of 1.3 to 1.7 minutes and 99.7% of the calls are answered in the range of 0.9 to 2.1 minutes.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Weights of Coffee Cans
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Example Weights of Coffee Cans
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections 7.4 and 7.5
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections 7.4 and 7.5
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections 7.4 and 7.5
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections 7.4 and 7.5
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections 7.4 and 7.5
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Quick Quiz Sections 7.4 and 7.5
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Chapter Test
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Chapter Test
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Chapter Test
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Chapter Test
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Chapter Test
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Chapter Test Solutions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Chapter Test Solutions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Chapter Test Solutions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide Chapter Test Solutions