Chapter 5 - Section 5.3 - The Fundamental Theorem of Calculus - 5.3 Exercises - Page 407: 31

$\frac{512}{15}$

$\displaystyle\int^{4}_{0}(t^{2}+t^{3/2})dt=\int^{4}_{0}t^{2}dt+ \int^{4}_{0}t^{3/2}dt$ $=\frac{t^{3}}{3}]^{4}_{0}+\frac{2}{5}t^{5/2}]^{4}_{0}$ $=\frac{1}{3}(4^{3}-0^{3})+\frac{2}{5}(4^{5/2}-0^{5/2})$ $=\frac{64}{3}+\frac{64}{5}=\frac{512}{15}$