Chapter 5 - Section 5.4 - Indefinite Integrals and the Net Change Theorem - 5.4 Exercises - Page 415: 30

$21$

$\int_0^8(\frac{1}{8}+\frac{1}{2}w+\frac{1}{3}w^{1/3})dw$ $=[\frac{1}{8}w+\frac{\frac{1}{2}}{1+1}w^{1+1}+\frac{\frac{1}{3}}{1/3+1}w^{1/3+1}]_0^8$ $=[\frac{w}{8}+\frac{w^2}{4}+\frac{w^{4/3}}{4}]_0^8$ $=(\frac{8}{8}+\frac{8^2}{4}+\frac{8^{4/3}}{4})-(\frac{0}{8}+\frac{0^2}{4}+\frac{0^{4/3}}{4})$ $=1+16+4-0$ $=21$