A function is defined by h(x)= cases 3x, & 0 x<2, 12-x^ 2 , & 2 x 5

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A function

h

is defined by

h(x)=\begin{cases} 3x, & 0\le x<2,\\ 12-x^{2}, & 2\le x\le 5. \end{cases}

Find the average value of

h

on the interval

[1,4]

. (a) Evaluate

\displaystyle \int_{1}^{4} h(x)\,dx

. (b) Using your result from part (a), determine the average value of

h

over

[1,4]

. Express your answer in exact form.