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Manipal MET2013MathematicsArea Under Curves

The area of the region [(x, y): x^2+y^2 1 x+y ] is;

Options

  1. A5
  2. B4
  3. C^2 3
  4. D4 - 1 2

Correct answer

D. 4 - 1 2

Step-by-step solution

x^2+y^2=1, x+y=1 meet when array rlrl & & x^2+(1-x)^2 & =1 & x^2+1+x^2-2 x & =1 & 2 x^2-2 x & =0 & & 2 x(x-1) & =0 array x=0, x=1 Meet at points A(1,0), B(0,1) Required area = 4 - 1 2 (1) (1)= 4 - 1 2 i . e ., [ quad. O A B- O A B]

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