Unit 5

Applications of Integration

The graded skill is the setup, not the antiderivative. Almost every lost mark here comes from the diagram, the slice, or the choice of variable.

Unit 5 practice

12 problems · Questions and worked solutions.

Lesson 5.1 · AP 8.1; 8.4–8.6

Choose a consistent slicing direction, locate intersections, and distinguish a function’s average value from an endpoint average.

Reading reference: Larson & Edwards §§7.1, 4.4

Lesson 5.2 · AP 8.2–8.3

Recover amounts from rates, split motion at direction changes, and distinguish net change from total variation.

Reading reference: Larson & Edwards §§4.4, 7.1

Lesson 5.3 · AP 8.9–8.12

Draw a perpendicular slice, measure radii from the actual rotation axis, and integrate cross-sectional area.

Reading reference: Larson & Edwards §7.2

Lesson 5.4 · AP 8.7–8.8

Convert the width of a base region into a cross-sectional area, then integrate that area through the solid.

Reading reference: Larson & Edwards §7.2

Unit 4: Integrals and the Fundamental Theorem

Unit 6: Techniques of Integration and Differential Equations

Work through questions with a tutor and get help with the steps you find difficult.