The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{1}{[\mathrm{x}]+4}\right) \mathrm{dx}$, where [•] denotes the greatest integer function, is

JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Definite Integrals

The value of

\int_{- \frac{π}{2}}^{\frac{π}{2}} (\frac{1}{[ x ] + 4}) dx

, where [•] denotes the greatest integer function, is

Answer: (C)

[- \frac{π}{2}, \frac{π}{2}]

the greatest integer

[x]

equals

- 2, - 1, 0, 1

[- \frac{π}{2}, - 1), [- 1, 0), [0, 1), [1, \frac{π}{2})

respectively. Hence

I = \frac{1}{2} (\frac{π}{2} - 1) + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} (\frac{π}{2} - 1) = \frac{7 π}{20} + (\frac{1}{3} + \frac{1}{4} - \frac{1}{2} - \frac{1}{5}) = \frac{7 π}{20} - \frac{7}{60} = \frac{7}{60} (3 π - 1) .

JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Single correct option

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