The function is defined piecewise by f(t)= cases t+1, & -2 t 0

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

Problem

The function

f

is defined piecewise by

f(t)=\begin{cases} t+1, & -2\le t\le 0,\\ t^{2}, & 0<t\le 3. \end{cases}

Let

g(x)=\int_{-2}^{x} f(t)\,dt

. What is the absolute maximum value of

g

on the closed interval

[-2,3]

? (a)

7.5

(b)

4.5

(c)

9

(d)

10