JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{1}{[ x ]+4}\right) dx\), where \([\bullet]\) denotes the greatest integer function, is
- A \(\frac{1}{60}(21\pi-1)\)
- B \(\frac{1}{60}(\pi-7)\)
- C \(\frac{7}{60}(3\pi-1)\)
- D \(\frac{7}{60}(\pi-3)\)
Answer & Solution
Correct Answer
(C) \(\frac{7}{60}(3\pi-1)\)
Step-by-step Solution
Detailed explanation
\(I =\int_{-\pi / 2}^{\pi / 2} \frac{1}{[ x ]+4} dx\) \(I =\int_{-\pi / 2}^{-1} \frac{ dx }{2}+\int_{-1}^0 \frac{ dx }{3}+\int_1^0 \frac{ dx }{4}+\int_1^{\pi / 2} \frac{ dx }{5}\)…
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