Work through the list without notes. Use a calculator only where a statement says so. 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 the radius of a disc is the distance from the axis of revolution to the curve, not from a coordinate axis. (Guide: “What changes when the axis moves”; Practice Q2, Q3)
- I can explain why spinning about y = k is like shifting the region down by k and spinning about the x-axis. (Guide: “A useful way to see it”)
- I can decide whether a region touches the axis along its whole length, and so whether discs apply. (Guide: “The axis must be part of the boundary”; Practice Q5(b), Q6(a))
Skills
- I can write the radius as larger minus smaller for an axis above, below, left or right of a curve. (Guide: radius table; Practice Q1, Q2)
- I can handle a negative axis such as y = −1, writing the radius as f(x) + 1. (Guide: Worked example 3)
- I can choose dx for a horizontal axis and dy for a vertical axis, rewriting the curve as x = g(y) when needed. (Guide: Worked example 2; Practice Q3, Q5(a), Q6(b))
- I can expand a squared radius such as (2 − y^(1/3))² and evaluate the volume exactly. (Practice Q5)
- I can write the integral in full and evaluate it with a calculator to three decimal places. (Practice Q4, Q6(c))
Reasoning
- I can explain why π ∫ [k² − f(x)²] dx is not a disc volume about y = k. (Practice Q1(A), Q4(C))
- I can find a disc radius from a graph by drawing one strip at right angles to the axis. (Guide: “Reading the radius from different representations”; Figure 1)
- I can check a volume against the smallest cylinder that contains the solid. (Guide: Worked examples 1 to 3; Practice Q7(c))
- I can explain what is wrong with an integral that uses the wrong variable or leaves out the curve. (Practice Q6(d))
All ticked? Move on to Topic 8.11, Volume with the Washer Method: Revolving Around the x- or y-Axis, or return to the Calculus AB roadmap or the Calculus BC roadmap.