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JEE Main202528 Jan 2025Evening ShiftMathematicsArea Under CurvesActual

The area of the region bounded by the curves x (1+y^2 )=1 and y^2=2 x is:

Options

  1. A2 ( 2 - 1 3 )
  2. B2 - 1 3
  3. C4 - 1 3
  4. D1 2 ( 2 - 1 3 )

Correct answer

B. 2 - 1 3

Step-by-step solution

aligned & x (1+y^2 )=1 & y^2=2 x aligned From equation (1) & (2) aligned x(1+2 x)=1 & 2 x^2+x-1=0 & x= 1 2 , x=-1 (Reject) & y^2=2 ( 1 2 ) & y= 1 aligned aligned Area bounded & = _ -1 ^1 ( 1 1+y^2 - y^2 2 ) d y & = . ( ⁻¹ y- y^3 6 ) |_ -1 ^1 & = 2 - 1 3 aligned

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