Answer
$\frac{7}{6}$
Work Step by Step
$\int_{0}^{1}\sqrt x(\sqrt x + 1) dx$
= $\int_{0}^{1} x+ \sqrt xdx$
= $\frac{1}{2} x^2 + \frac{2}{3}x^\frac{3}{2}|_{0}^{1}$
=$(\frac{1}{2} (1)^2 + \frac{2}{3}(1)^\frac{3}{2})-(\frac{1}{2} (0)^2 + \frac{2}{3}(0)^\frac{3}{2})$
=$(\frac{1}{2}+\frac{2}{3}) + 0$
=$\frac{7}{6}$
