Work through the list without notes. Use a calculator only where the linked question allows 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 how thin horizontal strips of length right − left and thickness Δy lead to an area integral in y. (Guide: “Turning the strips sideways”, Figure 1)
- I can explain why vertical and horizontal strips must give the same area for the same region. (Guide: Worked example 1 check; Practice Q3, Q7(b))
- I can explain why a negative result means I subtracted left minus right. (Guide: “Common misconceptions”; Practice Q2)
- I can look at a region and say whether dx or dy needs fewer integrals, and why. (Guide: “Choosing dx or dy”; Practice Q5(d))
Skills
- I can rewrite a curve given as y = f(x) in the form x = g(y). (Guide: Worked example 2; Practice Q3, Q7)
- I can find the y-limits by solving R(y) = L(y) algebraically. (Guide: Worked example 1; Practice Q2, Q5(a))
- I can decide which curve is on the right using a test y-value between the limits. (Guide: “The method, step by step”; Practice Q1, Q5(b))
- I can find intersections in y with a calculator, store them and use them as limits. (Guide: Worked example 3; Practice Q4, Q6(a))
- I can write an area integral with y-limits, brackets and dy before evaluating it. (Practice Q5(b), Q6(b))
Reasoning
- I can treat the y-axis as the curve x = 0 when it is a boundary. (Guide: Worked example 2; Practice Q1)
- I can interpret the length of a horizontal strip, R(y) − L(y), in a real context. (Practice Q6(d))
- I can use horizontal strips to find an area that would be hard with vertical strips. (Practice Q7)
All ticked? Move on to Topic 8.6, Finding the Area Between Curves That Intersect at More Than Two Points, or return to the Calculus AB roadmap or the Calculus BC roadmap.