A) 1
B) 1/2
C) 2
D) None of these
Correct Answer: B
Solution :
Let \[I=\int_{2}^{3}{\frac{\sqrt{x}}{\sqrt{5-x}+\sqrt{x}}dx}\] ... (i) \[\therefore \] \[I=\int_{2}^{3}{\frac{\sqrt{5-x}}{\sqrt{x}+\sqrt{5-x}}dx}\] ... (ii) On adding Eqs. (i) and (ii), we get \[2I=\frac{3\sqrt{x}+\sqrt{5-x}}{\sqrt{x}+\sqrt{5-x}}dx\] \[=\int_{2}^{3}{1\,\,dx}=3-2=1\] \[\Rightarrow \] \[I=\frac{1}{2}\]
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