CUET · MATHS · PYQ PAPER 2025
The value of \(\int_0^1[\log x-\log (1-x)] d x\) is
- A \(\frac{1}{2}\)
- B 2
- C 1
- D \(0\)
Answer & Solution
Correct Answer
(D) \(0\)
Step-by-step Solution
Detailed explanation
\(I = \int_0^1 [\log x-\log (1-x)] d x\) Let \(f(x) = \log x - \log(1-x)\). \(f(1-x) = \log(1-x) - \log(1-(1-x)) = \log(1-x) - \log x = -f(x)\) \(I = \int_0^1 f(x) dx = \int_0^1 f(1-x) dx = \int_0^1 -f(x) dx = -I\) \(2I = 0\) \(I = 0\)
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