COMEDK · Maths · 30. Definite Integration
\(\int_{1}^{e} \log x d x=\)
- A 1
- B \(e-1\)
- C \(e+1\)
- D 0
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
We have, \(\int_{1}^{e} \log x d x\) \(=\left[\log x \int 1 d x\right]_{1}^{e}-\int_{1}^{e}\left(\frac{d}{d x} \log x \int 1 d x\right) d x\) \(=[\log x \cdot x]_{1}^{e}-\int_{1}^{e} \frac{1}{x} \cdot x d x\) \(=[e \log e-1 \log (1)]-\int_{1}^{e} 1 d x\)…
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