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Calculating Area and Volume of Bounded Regions in Advanced Mathematics

This chapter focuses on understanding the principles of finding areas and volumes of various bounded regions through mathematical graphs. It covers specific problems and methods, including calculating the area between curves and using methods such as the washer method for solids of revolution. Key exercises include finding the volume of solids formed by revolving bounded regions about the x and y axes, as well as determining the area of regions bounded by certain functions. Each example aims to enhance problem-solving skills in calculus.

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Calculating Area and Volume of Bounded Regions in Advanced Mathematics

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  1. Review Chapter 6

  2. 1. Beginning AP Problem • 2. Homework • 3. Review/Homework Assignment • 4. Review Limits AGENDA

  3. Find the area of the region bounded by the graphs of and • 8 #1

  4. Find the area of the region bounded by the graphs of and • 125/6 #2

  5. Calculate the area of the regions bounded by the graphs 71/6 #3

  6. Find the volume of the solid formed by revolving the region bounded by about the y-axis. 4.099 #4

  7. Find the volume of the solid formed by revolving the region bounded by the graphs of • about the x-axis . 53.856 #5

  8. Use the washer method to find the volume of the solid of revolution formed by revolving the region bounded by about the x-axis. 251.327 #6

  9. Find the volume of the solid formed by revolving the region bounded by the graphs of about the line y=16. 1715.728 #7

  10. The base of a solid is the region bounded by the graphs of . Each cross section perpendicular to the x-axis is a triangle of altitude 2. Find the volume of the solid. • 10.667 #8

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