Let F(x)= _ 0 ^ x f(t) ,dt

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

Problem

Let

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

where

f(t)=\begin{cases} t^{2}, & t<2,\\ 5, & t\ge 2. \end{cases}

Which of the following describes

F'(x)

x=2

? (a)

F'(2)=5

(b)

F'(2)

does not exist because

f

is not continuous at

t=2

. (c)

F'(2)=4.5

(d)

F'(2)=\dfrac{8}{3}