MCQ
$\int_0^a {\frac{{x\,dx}}{{\sqrt {{a^2} + {x^2}} }}} = $
- ✓$a\,(\sqrt 2 - 1)$
- B$a\,(1 - \sqrt 2 )$
- C$a\,(1 + \sqrt 2 )$
- D$2a\sqrt 3 $
$\Rightarrow 2xdx = dt,$ then
$\int_0^a {\frac{{xdx}}{{\sqrt {{a^2} + {x^2}} }} = \frac{1}{2}\int_{{a^2}}^{2{a^2}} {\frac{1}{{\sqrt t }}dt} } $
$ = [{(2{a^2})^{1/2}} - {a^{2/2}}] = a(\sqrt 2 - 1)$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$f(x) = sin^{-1} \left( {\frac{{\,\,1 - \,\,\left| x \right|}}{3}} \right) + cos^{-1}\left( {\frac{{\left| x \right|\,\, - \,\,3}}{5}} \right)$ .
Then domain of $f(x)$ is given by :
"Maximize $z=x+4 y$
subject to $3 x+6 y \leq 6,4 x+8 y \geq 16$ and $x \geq 0, y \geq 0$."