The value of the integral, $\int_3^6 \frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}} d x$ is

The value of the integral, $\int_3^6 \frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}} d x$ is
  1. 1/2
  2. 3/2
  3. 2
  4. 1

Solution

$I=\int_3^6 \frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}} d x$ $I=\int_3^6 \frac{\sqrt{9-x}}{\sqrt{9-x}+\sqrt{x}} d x$ $2 I=\int_3^6 d x=3 \Rightarrow I=\frac{3}{2}$

Asked in: JEE Main 2006

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