If $\int_0^{\pi /2} {\frac{{\cot x}}{{\cot x + \cos {\rm{ec}}\,x}}} dx = m\left( {\pi + n} \right)$, then m.n is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\int_0^{\pi /2} {\frac{{\cot x}}{{\cot x + \cos \mathrm{ec}\,x}}} dx = m\left( {\pi + n} \right)

, then m.n is equal to

View answer and explanation

Correct option: D

- 1

Option D (-1) is correct because the integral evaluates to (π/2) - 1, which can be expressed as (1/2)(π - 2). Therefore, m = 1/2 and n = -2, and m*n = -1.

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