The value of the integral $\mathop \smallint \limits_{ - 1/2}^{1/2} \,\,{\left\{ {{{\left( {\frac{{x + 1}}{{x - 1}}} \right)}^2} + \,\,{{\left( {\frac{{x - 1}}{{x + 1}}} \right)}^2} - \,\,2} \right\}^{1/2}}dx$, is

$4\,\,\log \,\,\left( {\frac{3}{4}} \right)$

$\log \,\,\left( {\frac{3}{4}} \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of the integral

\int \limits_{ - 1/2}^{1/2} \,\,{\left\{ {{{\left( {\frac{{x + 1}}{{x - 1}}} \right)}^2} + \,\,{{\left( {\frac{{x - 1}}{{x + 1}}} \right)}^2} - \,\,2} \right\}^{1/2}}dx

, is

View answer and explanation

Correct option: C

4\,\,\log \,\,\left( {\frac{4}{3}} \right)

Option C,

4\,\,\log \,\,\left( {\frac{4}{3}} \right)

, is correct because it is the result of simplifying the integrand and evaluating the definite integral.

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