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MathsJEE Main 22 Jan 2026, Shift 1·Q15·MCQ·Easy–moderate

Definite Integration · Greatest integer function integral

The value of ∫−π2π2(1[x]+4)dx\displaystyle\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{1}{[x] + 4}\right)dx, where [∙][\bullet] denotes the greatest integer function, is
  1. (1)160(21π−1)\dfrac{1}{60}(21\pi - 1)
  2. (2)160(π−7)\dfrac{1}{60}(\pi - 7)
  3. (3)760(3π−1)\dfrac{7}{60}(3\pi - 1)
  4. (4)760(π−3)\dfrac{7}{60}(\pi - 3)

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