Unit 8: Applications of Integration

Area Between Curves:
Students will understand that the integral of (top - bottom) or (right - left) gives the precise area trapped between two functions.
Volumes of Solids with Known Cross-Sections: Students will learn how to find the volume of a 3D object whose base is a region in the xy-plane and whose "slices" are squares, triangles, or semi-circles.
Volumes of Revolution: Students will master the "Disk" and "Washer" methods to find the volume of objects created by spinning a 2D shape around an axis.
Average Value of a Function: Students will calculate the "average height" of a fluctuating curve over a specific interval.

8.1 Average Value of a Function on an Interval
8.2 Position, Velocity, and Acceleration Using Integrals
8.3 Using Accumulation Functions and Definite Integrals
in Applied Contexts
8.4 Area Between Curves (with respect to x)
8.5 Area Between Curves (with respect to y)
8.6 Area Between Curves - More than Two Intersections
8.7 Cross Sections: Squares and Rectangles
8.8 Cross Sections: Triangles and Semicircles
8.9 Disc Method: Revolving Around the x- or y- Axis
8.10 Disc Method: Revolving Around Other Axes
8.11 Washer Method: Revolving Around the x- or y-Axis
8.12 Washer Method: Revolving Around Other Axes

College Board AP Classroom Assessments