JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \([ t ]\) denotes the greatest integer \(\leq t\). Then \(\frac{2}{\pi} \int \limits_{\pi / 6}^{5 \pi / 6}(8[\operatorname{cosec} x]-5[\cot x]) d x\) is equal to
- A \(12\)
- B \(14\)
- C \(16\)
- D \(18\)
Answer & Solution
Correct Answer
(B) \(14\)
Step-by-step Solution
Detailed explanation
\(8 \int \limits_{\frac{\pi}{6}}^{\frac{5 \pi}{6}}[\operatorname{cosec} x] dx\) \(8 \int \limits_{\frac{\pi}{6}}^{\frac{5 \pi}{6}} dx =\frac{16 \pi / 3}{16 \pi / 3}\) \(I=\int \limits_{\frac{\pi}{6}}^{\frac{5 \pi}{6}}[\cot x] dx\) \(x \rightarrow \pi-x\)…
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