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Unformatted text preview: 4.2
4.3
4.5 A,B,C
C
A,B,C,D
A,B,C,D,E,F Suggested
Timeframe
(in blocks)
3 2 Course Objective(s)
Describe the definite integral
and all associated concepts. Student Objectives
•
•
• •
• Use the Fundamental Theorem of
Calculus to evaluate integrals
Understand that the “value” of a
definite integral describes the
‘displacement’
Practice the FTC with a variety of
functions including trigonometric,
logarithmic and exponential
functions.
Use usubstitution to evaluate
integrals; include ‘change of limits’
*Evaluate integrals using
‘integration by parts’ and ‘tabular
integration (optional) NJ CCCS Strands &
Indicators 4.1
4.2
4.3
4.5 A,B,C
C
A,B,C,D
A,B,C,D,E,F Suggested
Timeframe
(in blocks)
79 Course Objective(s)
Utilize various methods to
finding the area under a curve Student Objectives
•
• •
• Employ previous study of
integrals to basic applications •
• • • Distinguish between ‘displacement’
and ‘total distance’ when evaluating
a definite integral
Recognize that area “under the xaxis” has a negative value and apply
integration techniques such as
“splitting” to find total area
Finding the area between two
functions; include finding
intersection points
Use geometric approaches to finding
area given the graph of a function or
a complex integral; i.e..: semicircle,
Archimedes’ parabolic arch
Find the average value of a function
Find the total distance traveled and
the displacement of a particle or
other object over a given time
interval
Analyze ‘consumption’ problems
given a table of values; i.e..: how fuel
is consumed by a jet over a period of
time
Analyze ‘inandout’ problems; i.e.:
the number of attendees entering
and exiting an amusement park;
water flowing in and out of a holding
tank NJ CCCS Strands &
Indicators 4.1
4.2
4.3
4.5 A,B,C
C
A,B,C,D
A,B,C,D,E,F 4.1
4.2
4.3
4.5 A,B,C
C
A,B,C,D
A,B,C,D,E,F Suggested
Timeframe
(in blocks)
3 3 UNIT 6 – Applications of Integration
Course Objective(s)
Discuss approaches to finding
the volume of a solid Student Objectives
•
•
•
•
•
•
• Recall the method behind
rectangular approximations when
finding the area under a curve
Visualize and sketch the solid
created when revolving a given
region over the x axis or y  axis
Use the ‘disk method’ by integrating
the area of each slice (circle)
Find volume with respect to x and
with respect to y using the disk
method
Recall finding area between curves
and apply to finding the volume of a
‘washer’
*Find volume using the shell
method (optional)
Set up and evaluate integrals for all
methods NJ CCCS Strands &
Indicators 4.1
4.2
4.3
4.5 A,B,C
A,B,C,D
A,B,C,D
A,B,C,D,E,F Suggested
Timeframe
(in blocks)
45 Course Objective(s)
Introduce the volume of an
irregular threedimensional
solid using cross sections Student Objectives
•
•
• •
•
Introduce slope fields and
differential equations •
•
• Visualize and sketch the described
solid
Recall previous concept o...
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 Spring '10
 Zalla
 Calculus, AP Calculus

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