MathsJEE Main 21 Jan 2026, Shift 1·Q12·MCQ·Moderate

Definite Integration · Definite integral properties

The value of

\displaystyle\int_{-\pi/6}^{\pi/6}\left(\frac{\pi + 4x^{11}}{1 - \sin(\lvert x\rvert + \pi/6)}\right)dx

is equal to

(1) $2\pi$
(2) $4\pi$
(3) $8\pi$
(4) $6\pi$

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