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JEE Main2008MathematicsArea Under CurvesActual

The area of the plane region bounded by the curves x+2 y^2=0 and x+3 y^2=1 is equal to

Options

  1. A5 3
  2. B1 3
  3. C2 3
  4. D4 3

Correct answer

D. 4 3

Step-by-step solution

Solving the equations we get the points of intersection (-2,1) and (-2,-1) The bounded region is shown as shaded region. aligned & The required area =2 ₀^1 (1-3 y^2 )- (-2 y^2 ) & =2 ₀^1 (1-y^2 ) d y=2 [y- y^3 3 ]₀^1=2 2 3 = 4 3 . aligned

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