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: Physics Relationship

Unit 8: Applications of Antiderivatives Physics Relationships Identifier: Physics Relationship

The great part about these problems is that identifying them is usually straight forward. Most physics problems will use the language of position, velocity, and acceleration in the actual problem.

Additional language to look out for would be:

  • Speed = velocity
  • Decelerating = negative acceleration
  • Speeding up or slowing down = acceleration
  • Height of = position
  • Gravity = acceleration
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