# Use u substitution to evaluate integrals include

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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 u-substitution 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) 7-9 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..: semi-circle, 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 ‘in-and-out’ 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) 4-5 Course Objective(s) Introduce the volume of an irregular three-dimensional 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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