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Manipal MET2014MathematicsArea Under Curves

The area of the region bounded by 1-y^2=|x| and |x|+|y|=1 is

Options

  1. A1 / 3 sq unit
  2. B2 / 3 sq unit
  3. C4 / 3 sq units
  4. D1 sq unit

Correct answer

B. 2 / 3 sq unit

Step-by-step solution

aligned & Since, |x|+|y|=1 & array cll x+y=1, & x 0, & y 0 x-y=1, & x 0, & y 0 -x+y=1, & x 0, & y 0 -x-y=1, & x 0, & y 0 array . aligned and 1-y^2=|x| cases 1-y^2=x, & x 0 1-y^2=-x, & x 0 cases Required area aligned & array l = |2 ₀^1 (1-x) d x | + |2 _ -1 ^0 (x+1) d x |-4 ( 1 2 1 1 ) array & = 2 3 sq unit aligned

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