Work through the list without notes or a calculator. 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 ∫ (a to x) f(t) dt defines a function of x, and why the variable inside is a dummy variable. (Guide: “An integral that makes a new function”; Practice Q7(a))
- I can state the Fundamental Theorem of Calculus in the form d/dx ∫ (a to x) f(t) dt = f(x), including the continuity condition. (Guide: “The Fundamental Theorem of Calculus”; Practice Q6(a))
- I can explain why the theorem holds, using a thin strip of width h. (Guide: “Why it is true” and Figure 1; Practice Q7(c))
- I can explain why changing the constant lower limit does not change the derivative. (Guide: Worked example 1(c))
Skills
- I can find values of an accumulation function from a graph, using signed areas and reversing the sign when x is less than the starting value. (Guide: Worked example 1; Practice Q4, Q5(a), Q5(b))
- I can find the derivative of an accumulation function at a point by reading the height of f. (Guide: Worked example 1(b); Practice Q1, Q5(c))
- I can differentiate an integral whose lower limit is x. (Guide: Worked example 2(b); Practice Q2, Q7(d))
- I can differentiate an integral whose upper limit is a function of x, using the chain rule. (Guide: Worked example 2(c); Practice Q3, Q6(c))
- I can write a tangent line to a function defined by an integral and use it to estimate a value. (Guide: Worked example 3; Practice Q5(d), Q6(b))
Reasoning
- I can spot the errors of differentiating the integrand, dropping the chain-rule factor, or missing a minus sign. (Guide: “Common misconceptions”; Practice Q1, Q2, Q3, Q6(d))
- I can interpret an accumulation function and its derivative in context, with units. (Practice Q7)
All ticked? Move on to Topic 6.5, Interpreting the Behavior of Accumulation Functions Involving Area, or return to the Calculus AB roadmap or the Calculus BC roadmap.