Question
By using the properties of definite integrals, evaluate the integral $\int\limits_0^a {\frac{{\sqrt x }}{{\sqrt x + \sqrt {a - x} }}} dx$
$2I = \int\limits_0^a {\left( {\frac{{\sqrt x }}{{\sqrt x + \sqrt {a - x} }} + \frac{{\sqrt {a - x} }}{{\sqrt {a - x} + \sqrt x }}} \right)dx} $
$= \int\limits_0^a {\left( {\frac{{\sqrt x + \sqrt {a - x} }}{{\sqrt x + \sqrt {a - x} }}} \right)dx}$
$= \int\limits_0^a {1dx} = \left( x \right)_0^a = a$
$ \Rightarrow I = \frac{a}{2}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.