Chapter 5 - The Integral - 5.2 The Definite Integral - Exercises - Page 245: 38

$\frac{5}{4}$

$\int^{1/2}_{0}(12y^{2}+6y)dy$ $=12\int^{1/2}_{0}y^{2}dy+6\int^{1/2}_{0}ydy$ $=12\times\frac{(\frac{1}{2})^{3}}{3}+6\times\frac{(\frac{1}{2})^{2}}{2}$ $=12\times\frac{1}{24}+6\times\frac{1}{8}$ $=\frac{5}{4}$