WBJEE · Maths · Definite Integration
\(\int_{0}^{1} \log \left(\frac{1}{x}-1\right) d x\) is equal to
- A 1
- B 0
- C 2
- D None of the above
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
Let \(\quad I=\int_{0}^{1} \log \left(\frac{1}{x}-1\right) d x\) \(\therefore\) \(=\int_{0}^{1} \log \left(\frac{1-x}{x}\right) d x\) \(I=\int_{0}^{1} \log \left(\frac{x}{1-x}\right) d x=-1\) \(\quad\left[\because \int_{a}^{b} f(x) d x=\int_{a}^{b} f(a+b-x) d x\right]\)…
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