JEE Mains · Maths · STD 12 - 7.2 definite integral
The integral \(\int_{0}^{1} \frac{1}{{ }_{7}^{\left[\frac{1}{x}\right]}} d x=\) where [.] denotes the greatest integer function is equal to
- A \(1+6 \log _{e}\left(\frac{6}{7}\right)\)
- B \(1-6 \log _{e}\left(\frac{6}{7}\right)\)
- C \(\log _{e}\left(\frac{7}{6}\right)\)
- D \(1-7 \log _{ e }\left(\frac{6}{7}\right)\)
Answer & Solution
Correct Answer
(A) \(1+6 \log _{e}\left(\frac{6}{7}\right)\)
Step-by-step Solution
Detailed explanation
\(\int\limits_{0}^{1} \frac{1}{7\left[\frac{1}{x}\right]} dx =-\int\limits_{1}^{0} \frac{1}{\left.7^{\left[\frac{1}{x}\right.}\right]} dx\)…
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