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NDA 2017 Maths · Mathematics · Application of Integrals · medium

The area of the region bounded by y=ln x, the x-axis and the line x=e is

Single correct option

The area of the region bounded by y=ln⁡xy=\ln x, the xx-axis and the line x=ex=e is
  1. A. ee square units
  2. B. e−1e-1 square units
  3. C. 11 square unit
  4. D. 12\frac12 square unit
Show answer and solution

Answer: (C) 11 square unit

Area =∫1eln⁡x dx=[xln⁡x−x]1e=(e−e)−(0−1)=1=\int_1^e\ln x\,dx=\left[x\ln x-x\right]_1^e=(e-e)-(0-1)=1. The curve meets the axis at x=1x=1, so the lower limit is 11, not 00. The value e−1e-1 results from integrating 11 instead of ln⁡x\ln x.
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Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake