Question

Evaluate : $I=\underset{0}{\overset{\frac{1}{2}}{\int }}\frac{dx}{\sqrt{1-x}}$

Answer 1

$\begin{array}{c}I={\int }_0^{\frac{1}{2}}\frac{dx}{\sqrt{1-x}}\\ ={\int }_0^{\frac{1}{2}}{\left(1-x\right)}^{\frac{-1}{2}}dx\\ ={\left[\frac{2\sqrt{1-x}}{-1}\right]}_0^{\frac{1}{2}}\\ =\left(2-\sqrt{2}\right).\end{array}$