Work through the list without notes. Use a calculator only where a statement mentions one. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions. This topic is shared by Calculus AB and Calculus BC.
Understanding
- I can explain why a radius is a distance from the axis, written as larger coordinate minus smaller coordinate. (Guide: “The same washers, a different axis”; Practice Q1)
- I can explain why the lower curve gives the outer radius when the axis is above the region. (Guide: Figure 1; Practice Q2, Q6(b))
- I can explain why moving the axis changes each radius before squaring, so the volume cannot be adjusted by a simple amount. (Guide: Worked example 3 sense check)
Skills
- I can write radii for an axis y = k above or below a region, including axes such as y = −1. (Guide: Worked example 1 and “The same region, axis below”; Practice Q1, Q4)
- I can set up and evaluate a washer integral around a horizontal line other than the x-axis. (Guide: Worked example 1; Practice Q2, Q7(a))
- I can rewrite curves as x in terms of y and set up a washer integral around a vertical line x = h. (Guide: Worked example 2; Practice Q3, Q5, Q7(b))
- I can find intersection values on a calculator, store them and give a shifted-axis volume to three decimal places. (Guide: Worked example 3; Practice Q4, Q6(c))
- I can use a test point to check that my R and r match the sketch. (Guide: “A quick test before you integrate”)
Reasoning
- I can describe how the outer and inner boundaries swap when the axis moves from one side of a region to the other. (Guide: “The same region, axis below”; Practice Q6(d))
- I can check a volume against a cylinder, cone or frustum. (Guide: Worked example 2 check; Practice Q5(d))
- I can use symmetry to explain why two different axes give the same volume. (Practice Q7(c))
All ticked? This is the last topic of the Calculus AB course. Calculus BC students continue with arc length in Topic 8.13. Return to the Calculus AB roadmap or the Calculus BC roadmap to plan your revision.