Manipal MET2014MathematicsArea Under Curves
The area of the region bounded by 1-y^2=|x| and |x|+|y|=1 is
Options
- A1 / 3 sq unit
- B2 / 3 sq unit
- C4 / 3 sq units
- 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