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NTA Abhyas JEE Main2020MathematicsArea Under CurvesPractice

The area (in sq. units) bounded by y = ln ⁡ x , y = x e and the y -axis is equal to

Options

  1. Ae 2 - 1
  2. Be 2
  3. C5 e 2
  4. D3 e 2 - 1

Correct answer

B. e 2

Step-by-step solution

Note that y = x e is a tangent to y = ln ⁡ x at e , 1 Required Area = ∫ 0 e x e - ln ⁡ x d x = x 2 2 e - x ln ⁡ x + x 0 e = e 2 - e + e - 0 = e 2 sq. units

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