Use u substitution to evaluate integrals include

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online