CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The value of ∫ from 1 to e of log x dx (natural logarithm) is:
The antiderivative of log x is x log x − x. Evaluating from 1 to e gives (e − e) − (0 − 1) = 1. So the definite integral equals 1.
- A1Correct
- Be − 1
- Ce
- D0
Explanation
Write log x as 1·log x. By parts, ∫log x dx = x log x − x. At e: e·1 − e = 0. At 1: 0 − 1 = −1. The definite integral is 0 − (−1) = 1. The option e − 1 results from forgetting the −x term's effect on the lower limit.
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