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NTA Abhyas JEE Main2020MathematicsArea Under CurvesPractice

The area (in sq. units) bounded by the curve f x = e - x x ≥ 1 x - 1 + 1 e x < 1 and the x -axis is

Options

  1. A2 + 2 e 2
  2. B2 + 1 e 2
  3. C1 e 2
  4. D1 + 2 e 2

Correct answer

D. 1 + 2 e 2

Step-by-step solution

∵ Graph of f x is symmetric about x -axis, hence, Area = 2 ∫ 0 ∞ f x d x = 2 1 2 × 1 - 1 e 1 - 1 e + 1 2 × 1 e × 1 e + ∫ 1 ∞ e - x d x = 2 1 2 1 - 2 e + 2 e 2 + - e - x 1 ∞ = 1 - 2 e + 2 e 2 + 2 e = 1 + 2 e 2 sq. units

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