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The value of \({\int }_{−\frac{\pi }{2}}^{\frac{\pi }{2}}\left(\frac{1}{\left[x\right]+4}\right)dx\), where \(\left[\cdo…

Q1

The value of \({\int }_{−\frac{\pi }{2}}^{\frac{\pi }{2}}\left(\frac{1}{\left[x\right]+4}\right)dx\), where \(\left[\cdot \right]\) denotes the greatest integer function, is

a

\(\frac{7}{60}\left(\pi −3\right)\)

b

\(\frac{1}{60}\left(\pi −7\right)\)

c

\(\frac{7}{60}\left(3\pi −1\right)\)

d

\(\frac{1}{60}\left(21\pi −1\right)\)

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