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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $ \int \limits_3^5 \large\frac{\sqrt {\log (x)}}{\log (\theta- x)+ \log (x)}$$dx$

\[\begin {array} {1 1} (a)\;\frac{5}{2} \\ (b)\;\frac{3}{2} \\ (c)\;1 \\ (d)\;\frac{5}{4} \end {array}\]

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A)
$\int \limits_a^b \large\frac{f(x)}{f(a+b-x)+f(x)} $$dx=\large\frac{b-a}{2}$
By using the above formula
$a=3, b=5$
$a+b=8$
$\large\frac{b-a}{2}=\frac{5-3}{2}=1$
Hence the correct answer is c
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