Apentix/AP Calculus AB/Unit 8: Applications of Integration/Question

AP Calculus ABmediummcq1 pt

Let $g(x)=\int_0^x f(t)\,dt$ , where $f$ is a linear function with $f(0)=2$ and $f(3)=8$ . What is $g(3)$ ?

A.

24

B.

6

C.

30

D.

15

Explanation

Core Concept

$g(3)$ is the area under $f$ on $[0,3]$ , a trapezoid of height 3 with parallel sides 2 and 8. Its area is $\frac{2+8}{2}\cdot 3=15$ .

Correct Answer

D $15$

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