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: Mean Value Theorem for Definite Integrals

Unit 8: Applications of Antiderivatives Mean Value Theorem for Definite Integrals Identifier: Mean Value Theorem for Definite Integrals

The language of the problem will usually be very specific, “Find the value(s) of c that satisfy the Mean Value Theorem for integrals…”. The language must be specific so that you know that you are looking to find the actual x-value, and not just the Average Value, which is a y-value.

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