Unit 8: Applications of Antiderivatives

Max-Min Inequality Rule for Definite Integrals
3 Topics
Identifier: Max-Min Inequality Rule for Definite Integrals
Method: Max-Min Inequality Rule for Definite Integrals
Example 1: Max-Min Inequality for Definite Integrals
Average Value
3 Topics
Identifier: Average Value
Method: Average Value
Example 1: Average Value Integral
Mean Value Theorem for Definite Integrals
4 Topics
Extension of Mean Value Theorem for Definite Integrals
Identifier: Mean Value Theorem for Definite Integrals
Method: Mean Value Theorem for Definite Integrals
Example 1: Mean Value Theorem for Definite Integrals
Accumulation Tool
3 Topics
Identifier: Integral as Accumulation Tool
Method: Integral as Accumulation Tool
Example 1: Integral as Accumulation Tool
Physics Relationships
3 Topics
Identifier: Physics Relationship
Method: Physics Relationships
Example 1: Physics Relationship
Displacement vs. Distance Traveled
3 Topics
Identifier: Distance vs. Displacement
Method: Distance vs. Displacement
Example 1: Distance vs. Displacement
Area Between Two Curves = Region Bounded by Two Curves
5 Topics
Identifier: Area Between Two Curves
Method: Area Between Two Curves
Example 1: Area Between Two Curves (No Calculator Allowed)
Example 2: Area Between Two Curves (Calculator Allowed)
Example 3: In Terms of y (No Calculator Allowed)
Volumes of Solids
Using Cross Sectional Areas
3 Topics
Identifier: Cross Sectional Areas
Method: Cross Sectional Areas
Example 1: Cross Sectional Areas
Disk Method
4 Topics
Identifier: Disk Method
Method: Disk Method
Example 1: About the x-axis
Example 2: About an axis other than the x-axis
Washer Method
3 Topics
Identifier: Washer Method
Method: Washer Method
Example 1: Washer Method About the x-axis
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Identifier: Cross Sectional Areas

Unit 8: Applications of Antiderivatives Using Cross Sectional Areas Identifier: Cross Sectional Areas

The language that is used to identify these types of problems must be very specific because this is a very specific use case. When they want you to apply this cross-sectional area method, they will be very direct with the language, and you should expect to see the term “cross-section” used.

  • “the cross-section perpendicular to the x-axis has area…”
  • “the cross-sections are equilateral triangles”

Other language to be aware of is the use of the term “solid”. They use the wording “solid” when they are wanting you to find the “volume” of a shape.

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