Answer
=$ 0.353$
Work Step by Step
$\int^1_0c\sqrt x(1-x)dx$
=$c(\frac{2}{3}x^\frac{3}{2}-\frac{2}{5}x^\frac{5}{2})]^1_0$
=$\frac{4}{15}c$,
So,
$c$=$\frac{15}{4}$.
Then
$\int^\frac{1}{2}_\frac{1}{4}\frac{15}{4}\sqrt x(1-x)dx$
=$\frac{7}{16}\sqrt 2-\frac{17}{64}$
=$0.353$
