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AP EAMCET2013MathematicsArea Under Curves

The area (in sq units) bounded by the curves x=-2 y^2 and x=1-3 y^2 is

Options

  1. A2 3
  2. B1
  3. C2 3
  4. D2 3

Correct answer

C. 2 3

Step-by-step solution

Given curves, and aligned & x=-2 y^2 & x=1-3 y^2 aligned On solving both curves, we get gathered -2 y^2=1-3 y^2 y= 1 and x=-2 gathered So, the intersection points are (-2,1) and (-2,-1) . Required area aligned & =2 ₀^1 (1-3 y^2 )- (-2 y^2 ) d y & =2 ₀^1 (1-y^2 ) d y & =2 (y- y^3 3 )₀^1=2 (1- 1 3 ) & =2 2 3 = 4 3 aligned

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