7.8 Volumes With Cross Sectionsap Calculus



From calculus, we know the volume of an irregular solid can be determined by evaluating the following integral: Where A(x) is an equation for the cross-sectional area of the solid at any point x. We know our bounds for the integral are x=1 and x=4, as given in the problem, so now all we need is to find the expression A(x) for the area of our solid.

1) Watch & note Brightstorm’s AP Calculus video: Volume – Cross Sections to the 13:43 mark only. 2) Complete the attached Pre-Quiz: Square & Rectangular Cross Sections Watch Spencer Munroe (APC '14) explain #1 from Pre- Quiz here. Table of Contents and Introduction: General Overview of Calculus Chapter 1: Review of Derivatives Chapter 1 pdf 1.1: The Power and Exponential Rules with the Chain Rule; 1.2: Trig, Trig Inverse, and Log Rules; 1.3: Local Linearity, Euler’s Method, and Approximations.

Volumes

7.8 Volumes With Cross Sectionsap Calculus 2nd Edition

Calculus Chapters 7 & 8


  • Chapter 7 unassigned problems that would be good review for test:
Chapter 7 Extra Practice Worksheets
  • Slope Fields Worksheet and Key
Chapter 7 Help Links
  • Related Rates Video 1 (approaching cars)
  • Related Rates Video 2 (ladder)
  • Related Rates Video 3 (volume)
  • Related Rates Video 4 (shadow)
  • Related Rates Video 5 (hot air balloon)
  • U-Sub Videos (Khan Academy)
  • U-Sub Video (Not Khan)

(answers at the end of each link)
  • Volumes of Solids Worksheet 1 (Pick a Method)
  • Volumes of Solids Worksheet 2 (Washer and Disks)
  • Volumes of Solids Worksheet 3 (Shells)
  • Volumes of Solids Worksheet 4 (Cross Sections)