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JEE Main201910 Jan 2019Morning ShiftMathematicsDefinite IntegrationActual

Let I = ∫ a b x 4 - 2 x 2 d x . If I is minimum then the ordered pair ( a , b ) is

Options

  1. A0 ,   2
  2. B2 , - 2
  3. C- 2 , 0
  4. D- 2 , 2

Correct answer

D. - 2 , 2

Step-by-step solution

Given that, I = ∫ a b x 4 - 2 x 2 d x Let f x = x 4 - 2 x 2 To draw it's graph, finding the points where it intersects the x -axis, put f x = 0 ⇒ x 4 - 2 x 2 = 0 ⇒ x 2 x 2 - 2 = 0 So, x = 0 and x = ± 2 . The graph of f x is, From the figure, we get minimum area when - 2 ≤ x ≤ 2 . Hence, the ordered pair can be written as a ,   b = - 2 ,   2 .

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