The value of the integral ∫_(-π/2)^(π/2) 1/([x]+4) dx, where [·]… | JEE Main 2026 Mathematics PYQ | Jeeify

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MCQMediumJEE Main 2026 · 22 January, Shift 1Definite Integrals

The value of the integral $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{1}{[x]+4}\,dx,$ where $[\cdot]$ denotes the greatest integer function, is

A
$\dfrac{1}{60}(\pi-7)$
B
$\dfrac{1}{60}(21\pi-1)$
C
$\dfrac{7}{60}(3\pi-1)$
D
$\dfrac{7}{60}(\pi-3)$

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