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NTA Abhyas JEE Main2020MathematicsArea Under CurvesPractice

The area of the region enclosed by f x = - 2 x e x and the x -axis is

Options

  1. A1 sq. unit
  2. B2 sq. units
  3. C1 2 sq. unit
  4. Dnot defined

Correct answer

B. 2 sq. units

Step-by-step solution

f x = - 2 x e - x f ' x = 2 x e - x - 2 e - x = 2 e - x x - 1 Area = ∫ 0 ∞ - 2 x e - x d x = 2 ∫ 0 ∞ x e - x d x = - x e - x 0 ∞ + ∫ 0 ∞ e - x d x = 2 0 - e - x 0 ∞ = 2 × 1 = 2

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