AP Calculus BC 6.6 Definite Integral Properties Overview

}

$g(-6)=\int_{0}^{-6} f(t) d t=-\int_{-6}^{0} f(t) d t=-12$

g(-6)

1 point

$g(4)=\int_{0}^{4} f(t) d t=\frac{1}{2} \cdot 4 \cdot 2=4$

g(4)

1 point

$g(6)=\int_{0}^{6} f(t) d t=\frac{1}{2} \cdot 4 \cdot 2-\frac{1}{2} \cdot 2 \cdot 1=3$

g(6)

1 point

Scoring notes:

- Supporting work is not required for any of these values. However, any supporting work that is

shown must be correct to earn the corresponding point.

- Special case: A response that explicitly presents $g(x)=\int_{-6}^{x} f(t) d t$ does not earn the first point it

would have otherwise earned. The response is eligible for all subsequent points for correct answers,

or for consistent answers with supporting work.

○ Note: $\int_{-6}^{-6} f(t) d t=0, \int_{-6}^{4} f(t) d t=16, \int_{-6}^{6} f(t) d t=15$

- Labeled values may be presented in any order. Unlabeled values are read from left to right and

from top to bottom as g(-6), g(4), and g(6), respectively. A response that presents only 1 or 2

values must label them to earn any points.

Total for part (a) 3 points