Consider the function p(x)= cases x^ 2 -4,&1 x<2 +2,&2 x 3 cases

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider the function

p(x)=\begin{cases}x^{2}-4,&1\le x<2\\bx+2,&2\le x\le 3\end{cases},

where

b

is a real constant. For which value of

b

is the average value of

p

[1,3]

equal to

1

? (a)

\dfrac{4}{15}

(b)

\dfrac{16}{15}

(c)

\dfrac{2}{3}

(d)

1