Chapter 16, Problem 5RE

Determine whether each of the following statements is true or false, and explain why.

5.    The average value of the function f(x) = 2x² + 3 on [1, 4] is given by

$\frac{1}{3}{\displaystyle {\int }_1^4\pi {\left(2x^2+3\right)}^{2}dx.}$