Let be continuous on and suppose for and for

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

Problem

Let

g

be continuous on

[2,8]

and suppose

g(t)>0

for

2<t<5

and

g(t)<0

for

5<t<8

. Define

G(x)=\displaystyle\int_{2}^{x} g(t)\,dt

. Which statement best describes the behavior of

G

on the interval

(2,8)

? (a)

G

is increasing everywhere on

(2,8)

because the interval of integration is expanding. (b)

G

is constant on

(2,5)

and decreases on

(5,8)

. (c)

G

is increasing on

(2,5)

and decreasing on

(5,8)

. (d)

G

is decreasing on

(2,5)

and increasing on

(5,8)