Let h(x)= cases 3,&0 x<1 +1,&1 x 3 cases where is a constant

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

Problem

Let

h(x)=\begin{cases}3,&0\le x<1\\ax+1,&1\le x\le 3\end{cases}

where

a

is a constant. If the average value of

h

[0,3]

4

, what is the value of

a

? (a)

\dfrac{4}{3}

(b)

\dfrac{7}{8}

(c)

\dfrac{7}{4}

(d)

\dfrac{3}{2}