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Applications of Integration

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A series of free Calculus Video Lessons from UMKC - The University of Missouri-Kansas City.

Calculus I - Lecture 29

Plane Area 

  • Area Between Two Curves [One Floor, One Ceiling] [11 min.]
  • Area Between Two Curves [One Left, One Right] [7.5 min.]
  • An Exercise [5.5 min.]

Calculus I - Lecture 29 Part II - The Definite Integral Applied: Volumes I

Volumes I 

  • Volumes by Slicing [12.5 min.]
  • Volumes of Solids of Revolution: Disks [15.5 min.]
  • Volumes of Solids of Revolution: Washers [12 min.]
  • Some Exercises [8.5 min.]

Calculus I - Lecture 30

Volumes II 

  • Volumes of Solids of Revolution: Cylindrical Shells [14.5 min.]
  • An Exercise [6 min.]

Length of a Plane Curve 

  • Finding Arc Lengths [11.5 min.]
  • Finding Arc Lengths of Parametric Curves [6.5 min.]
Calculus I - Lecture 31

Average Value of a Function 

  • Average (Mean) Value of a Continuous Function [13 min.]


  • Work Done by a Constant Force [3 min.]
  • Work Done by a Variable Force [13.5 min.]
  • Do-It-Yourself Integrals: Pumping Fluids [8 min.]
  • Work as Change in Kinetic Energy [6 min.]
  • An Exercise [5 min.]


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