Let be continuous on with for and for

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

f

be continuous on

0 \le x \le 8

with

f(x) > 0

for

0 < x < 4

and

f(x) < 0

for

4 < x < 8

. Define the accumulation function

F(x)=\displaystyle\int_{0}^{x} f(t)\,dt

for

0 \le x \le 8

. Which of the following best describes the monotonic behavior of

F

(0,8)

? (a)

F

is decreasing on

(0,4)

and increasing on

(4,8)

. (b)

F

is increasing on

(0,8)

. (c)

F

is increasing on

(0,4)

and decreasing on

(4,8)

. (d)

F

is increasing on

(0,4)

and constant on

(4,8)