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)$.
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