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MathsJEE Main 28 Jan 2026, Shift 2·Q13·MCQ·Moderate

Definite Integration · Greatest integer function integral

Let [⋅][\cdot] denote the greatest integer function. Then ∫−π2π2(12(3+[x])3+[sin⁡x]+[cos⁡x])dx\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\dfrac{12(3 + [x])}{3 + [\sin x] + [\cos x]}\right)dx is equal to:
  1. (1)15π+415\pi + 4
  2. (2)11π+211\pi + 2
  3. (3)13π+113\pi + 1
  4. (4)12π+512\pi + 5

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