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JEE Main20198 Apr 2019Evening ShiftMathematicsArea Under CurvesActual

Let S α = x , y : y 2 ≤ x , 0 ≤ x ≤ α and A α is area of the region S α . If for a λ , 0 < λ < 4 , A λ : A 4 = 2 : 5 , then λ equals:

Options

  1. A4 2 5 1 3
  2. B2 4 25 1 3
  3. C4 4 25 1 3
  4. D2 2 5 1 3

Correct answer

C. 4 4 25 1 3

Step-by-step solution

S λ = 2 ∫ 0 λ x d x = 2 x 3 2 3 2 0 λ = 4 3 λ 3 2 ∴ S 4 = 4 3 4 3 2 Given S λ S 4 = 2 5 ⇒ λ 3 2 4 3 2 = 2 5 ⇒ λ = 4 4 25 1 3

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