AP Calculus AB · Unit 8
Applications of Integration
In short
Unit 8: Applications of Integration in AP Calculus AB covers 12 topics: Finding the Average Value of a Function on an Interval, Connecting Position, Velocity, and Acceleration of Functions Using Integrals, Using Accumulation Functions and Definite Integrals in Applied Contexts, Finding the Area Between Curves Expressed as Functions of x and 8 more. Open each one for what you need to know, a self-check list and how it is tested on the exam.
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What is in Unit 8: Applications of Integration?
Unit 8: Applications of Integration
8.1 Finding the Average Value of a Function on an Interval
- I can apply the formula 1/(b-a) ∫ f(x)dx to find the average value of a continuous function.
8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
- I can use the definite integral of velocity to find a particle's displacement and the definite integral of speed to find its total distance traveled over an interval of time.
8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
- I can interpret the meaning of a definite integral in the context of an accumulation problem.
- I can determine the net change of a quantity using definite integrals in applied contexts.
8.4 Finding the Area Between Curves Expressed as Functions of x
8.5 Finding the Area Between Curves Expressed as Functions of y
- I can calculate the area of a region in the plane by setting up and evaluating a definite integral with respect to y.
8.6 Finding the Area Between Curves That Intersect at More Than Two Points
- I can calculate the area between curves that intersect at more than two points by using a sum of definite integrals or the absolute value of their difference.
8.7 Volumes with Cross Sections: Squares and Rectangles
8.8 Volumes with Cross Sections: Triangles and Semicircles
- I can find the volume of a solid with triangular cross sections using definite integrals and the area formula for a triangle.
- I can find the volume of a solid with semicircular and other geometrically defined cross sections using definite integrals and the appropriate area formulas.
8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
8.10 Volume with Disc Method: Revolving Around Other Axes
8.11 Volume with Washer Method: Revolving Around the x- or y-Axis
8.12 Volume with Washer Method: Revolving Around Other Axes
- I can find the volume of a solid of revolution around any horizontal or vertical line using the washer method.
Applications of Integration: common questions
What is in Unit 8: Applications of Integration?
It covers 12 topics: 8.1 Finding the Average Value of a Function on an Interval; 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals; 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts; 8.4 Finding the Area Between Curves Expressed as Functions of x; 8.5 Finding the Area Between Curves Expressed as Functions of y; 8.6 Finding the Area Between Curves That Intersect at More Than Two Points; 8.7 Volumes with Cross Sections: Squares and Rectangles; 8.8 Volumes with Cross Sections: Triangles and Semicircles; 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis; 8.10 Volume with Disc Method: Revolving Around Other Axes; 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis; 8.12 Volume with Washer Method: Revolving Around Other Axes.
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