The value of $\mathop \smallint \limits_0^{\pi /2} \,{\rm{cosec}}\;\,\,\left( {x - \pi /3} \right)\,\,{\rm{cosec}}\,\,\left( {x\,\, - \,\,\pi /6} \right)dx$, is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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The value of

\int \limits_0^{\pi /2} \,\mathrm{cosec}\;\,\,\left( {x - \pi /3} \right)\,\,\mathrm{cosec}\,\,\left( {x\,\, - \,\,\pi /6} \right)dx

, is

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Correct option: B

- \,2\,\,\log \,\,3

Option B (-2 log 3) is correct because the integral simplifies using trigonometric identities and evaluates to -2 log 3 after applying the limits.

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