Chapter 4 - Integration - 4.8 Average Value Of A Function And It's Applications - Exercises Set 4.8 - Page 335: 4

See explanation.

Using the average value equation: $=\frac{1}{-(-1)+8} \int_{-1}^{8} x^{1 / 3} d x=\left[\frac{3}{4} x^{4 / 3}\right]_{-1}^{8}.\frac{1}{9}=[-(-1) \sqrt[3]{-1}+8 \sqrt[3]{8}]\frac{1}{12}$ $=[-1+16]\frac{1}{12}=\frac{15}{12}=\frac{5}{4}$