Let , where is continuous. Suppose for and for . Determine the open intervals within…

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

F(x)=\displaystyle\int_{2}^{x} f(t)\,dt

, where

f

is continuous. Suppose

f(t)>0

for

3<t<6

and

f(t)<0

for

6<t<8

. Determine the open intervals within

(3,8)

on which

F

is increasing and the intervals on which

F

is decreasing.