Area and Volumes of Revolution

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Area and Volumes of Revolution

  1. 1. AP Calculus AB/BC<br />Area & Volume<br />
  2. 2. Area & Volume<br />Larson 6.1, 6.2, 6.3, FDWK 7.2, 7.3<br />Area Between Two Curves<br />Area Between Intersecting Curves<br />Area With Respect to 𝑦<br />Volumes of Revolution – Disks<br />Volumes of Revolution – Washers<br />Volumes of Revolution – Cylindrical Shells<br />Solids With Known Cross-Sections<br />Β <br />
  3. 3. Area Between Two Curves<br />
  4. 4. Example 1<br />Sketch the region bounded by the graphs of the algebraic functions <br />𝑦=sinπ‘₯<br />𝑦=π‘₯Β <br />π‘₯=πœ‹2<br />π‘₯=πœ‹<br />and find the area of the region.<br />Β <br />
  5. 5. Click here for video<br />
  6. 6. Example 2<br />Sketch the region bounded by the graphs of the algebraic functions <br />𝑦=π‘₯2βˆ’4π‘₯<br />𝑦=2π‘₯<br />and find the area of the region.<br />Β <br />
  7. 7. Click here for video<br />
  8. 8. Example 3<br />Find the area enclosed between the graphs of<br />𝑦=π‘₯4βˆ’4π‘₯2+4<br />𝑦=π‘₯2<br />Β <br />
  9. 9. Click here for 1st video<br />Click here for 2nd video<br />
  10. 10. Click here for video<br />
  11. 11. Example 4<br />Find the volume of the solid formed by revolving the region bounded by the π‘₯-axis, the graph of 𝑓π‘₯=12π‘₯2 and the line π‘₯=2 about the π‘₯-axis.<br />Β <br />
  12. 12. Click here for video<br />
  13. 13. Example 5<br />Find the volume of the solid formed by revolving the region bounded by the graphs of 𝑓π‘₯=π‘₯2 and 𝑔π‘₯=π‘₯3 about the π‘₯-axis.<br />Β <br />
  14. 14. Click here for video<br />

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