# 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

• 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.]

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 