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Manipal MET2021MathematicsArea Under Curves

The area included between the curves y^2=2 x and x^2=2 y is

Options

  1. A3 4 sq unit
  2. B4 3 sq unit
  3. C1 2 squnit
  4. D4 3 sq unit

Correct answer

B. 4 3 sq unit

Step-by-step solution

The point of intersection of the curves y^2=2 x and x^2=2 y are O(0,0), A(2,2) . Required area = ₀^2 ( 2 x - x^2 2 ) d x aligned & = [ 2 x^ 3 / 2 3 / 2 - x^3 6 ]₀^2 & = [ 2 3 2^2- 2^3 6 ]= [ 8 3 - 4 3 ] & = 4 3 sq unit aligned

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