Answer
$\frac{b^{2}}{4}$
Work Step by Step
$\int^{b}_{0}\frac{x}{2}dx=\frac{1}{2}\int^{b}_{0}xdx$
$=\frac{1}{2}\times\frac{b^{2}}{2}= \frac{b^{2}}{4}$
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