MCQ
$\mathop \smallint \limits_3^6 \frac{{\sqrt x }}{{\sqrt {9 - x} + \sqrt x }}\;dx = $
- A$\frac{1}{2}$
- ✓$\frac{3}{2}$
- C$2$
- D$1$
$=\int_{3}^{6} \frac{\sqrt{9-x}}{\sqrt{9-9+x}+\sqrt{9-x}} d x$
$\Rightarrow I=\int_{3}^{6} \frac{\sqrt{9-x}}{\sqrt{x}+\sqrt{9-x}} d x \ldots(i i)$
On adding Eqs. (i) and (ii), we get
$2 I=\int_{3}^{6} \frac{\sqrt{x}+\sqrt{9-x}}{\sqrt{x}+\sqrt{9-x}} d x$
$=\int_{3}^{6} 1 d x=[x]_{3}^{6}$
$=6-3=3$
$\Rightarrow I=\frac{3}{2}$
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