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NTA Abhyas JEE Main2020MathematicsArea Under CurvesPractice

The area bounded by the curve y = x 2 x - 1 2 with the x -axis is k sq. units, then the value of 60 k is equal to

Options

  1. A1
  2. B2
  3. C1 2
  4. D1 4

Correct answer

B. 2

Step-by-step solution

The required area is A = ∫ 0 1 x 2 x - 1 2 d x or A = ∫ 0 1 x 2 - x 2 d x = ∫ 0 1 x 4 + x 2 - 2 x 3 d x = x 5 5 + x 3 3 - 2 x 4 4 0 1 = 1 5 + 1 3 - 2 4 = 1 30 = k ∴ 60 k = 2

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