AP Calculus BC 6.1: Accumulation of Change

Practice AP Calculus BC questions on interpreting signed area under a rate graph as accumulated change with appropriate units.

[Maximum number: 2]

The continuous function f is defined on the closed interval $-6 \leq x \leq 12$ . The graph of f,

consisting of two semicircles and one line segment, is shown in the figure.

$Graph of $f$$

Graph of $f$

Let g be the function defined by $g(x)=\int_{6}^{x} f(t) d t$ .

Find g(12) and g(0). Label your answers.

C Find g(12) and g(0). Label your answers.

$g(12)=\int_{6}^{12} f(t) d t=\frac{1}{2} \cdot 6 \cdot 3=9$	g(12)	Point 5 (P5)
$g(0)=\int_{6}^{0} f(x) d x=-\int_{0}^{6} f(x) d x=-\frac{\pi}{2} 3^{2}=-\frac{9 \pi}{2}$	g(0)	Point 6 (P6)

Scoring Notes for Part C

- Unlabeled values do not earn either P5 or P6.

- P5 is earned for a response of g(12)=9, with or without supporting work.

- P6 is earned for a response of $g(0)=-\frac{9 \pi}{2}$ , with or without supporting work.

Note: Incorrect communication between the label " g(0) " and the answer will be treated as scratch

work and will not impact scoring. For example, $g(0)=\int_{0}^{6} f(x) d x=-\frac{9 \pi}{2}$ earns P6.

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CHA-4.A—Interpret the meaning of areas associated with the graph of a rate of change in context question 1