JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \(\int\limits_{ - \pi /2}^{\pi /2} {\frac{{dx}}{{\left[ x \right] + \left[ {\sin \,x} \right] + 4}}} \) where \([t]\) denotes the greatest integer less than or equal to \(t\), is
- A \(\frac{1}{{12}}\left( {7\pi + 5} \right)\)
- B \(\frac{1}{{12}}\left( {7\pi - 5} \right)\)
- C \(\frac{3}{{20}}\left( {4\pi - 3} \right)\)
- D \(\frac{3}{{10}}\left( {4\pi - 3} \right)\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{{20}}\left( {4\pi - 3} \right)\)
Step-by-step Solution
Detailed explanation
\(\int_{-\pi / 2}^{\pi / 2} \frac{d x}{[x]+[\sin x]+4}\) \(=\int_{-\pi / 2}^{0} \frac{d x}{[x]+-1+4}+\int_{0}^{\frac{\pi}{2}} \frac{d x}{[x]+4}\)…
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