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NTA Abhyas JEE Main2020MathematicsArea Under CurvesPractice

The area bounded by the curves y = x 2 and y = 2 1 + x 2 is

Options

  1. A( π − 1 3 ) sq. units
  2. B( π − 2 3 ) sq. units
  3. C( 2 π − 1 ) 3 sq. units
  4. DNone of these

Correct answer

B. ( π − 2 3 ) sq. units

Step-by-step solution

For point of intersection x 2 = 2 1 + x 2 ⇒ x 4 + x 2 - 2 = 0 ⇒ x 2 - 1 x 2 + 2 = 0 ⇒ x = 1 , - 1 , ⇒ y = 1 , -1 ∴ a r e a = 2 ∫ 0 1 2 1 + x 2 - x 2 d x = 4 tan - 1 ⁡ x 0 1 - 2 3 x 3 0 1 = 4 π / 4 - 2 / 3 = π - 2 / 3

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