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05 Applications of Integration

 
Applications of Integration
5.1 Can compute the area between curves
5.2 Can compute volumes of revolution using disks
5.5 Can compute the average value of a function


 

Chapter 5 - Applications of Integration

 

5.1 More About Areas

·    Appropriate integrals are used in a variety of applications to model physical, social, or economic situations.

·    Specific application should include finding the area of a region.

The area under a curve and between two curves can be interpreted in many powerful ways. We’ll learn how to apply this simple area concept to very different real world situations.

The Area Between Curves

KHW: Area Between Curves

5.2 Volumes via Cross-sections and Rings

·    Finding the volume of a solid with known cross-sections.

·    Volumes of solids of revolution.

We’ll learn how to find the volumes of complex shapes using calculus. These shapes can often times be hard to pictures, so we’ll build real-world models, and 3D computer models to better understand them.

Volumes of Solids of Revolution: Disks and Rings (12 Videos)

KHW: Disks and Rings

Volume of a Solid with Known Cross-Section

KHW: Cross Sections

5.3 Volumes via Cylindrical Shells

·    The method of cylindrical shells to compute volumes of revolution.

·    Comparisons between the shell and washer methods.

We’ll use the natural symmetries of rotation to find the volumes of even more solids.

Volumes of Solids of Revolution: Cylindrical Shells (7 videos)

KHW: Shells

 5.4 Work
·    Computing the amount of work (in the Physics sense) done in a system.

Integrating Newton's Second Law of Motion, F=ma, allows us to compute how much work is done moving an object.
 

5.5 The Average Value of a Function

·    Finding the average value of a function and the Mean Value Theorem.

·    A geometric interpretation of the MVT for integrals.

We know how to find the average rate of change of a function. What does it mean to find the average value of a function?

The Mean Value Theorem for Integrals (4 Videos)

KHW: Mean Value of Functions





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5A  [u5.1: 1, 3, 5, 9, 11, 13, 17, 19, 27, 31, 35, 37, 46][u5.2: 1, 5, 7, 9, 11, 13, 15, 25, 29, 49] 
5B [u5.3: 1, 5, 7, 9, 13, 15, 17, 21, 37, 39, 45, 47] 
5C [u5.4: 1, 3, 7, 9, 11, 13, 15, 19, 21] [u5.5: 1, 7, 9, 11, 13, 17, 19] 
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Nikhil Joshi,
Feb 9, 2018, 7:47 AM