Find the area of the closed curve bounded by these equations.
You have four equations.
y |y| + x |x| = 1
y |y| - x |x| = 1
y |y| + x |x| = -1
y |y| - x |x| = -1
Find the area of the closed disjoint curve bounded by these equations.
The answer is 3.142.
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The first equation, in the first quadrant, is the equation of a circle.
It is the equation of hyperbola for the 2nd and 4th quadrant. These hyperbolas stretch to infinity. (the equation isn't defined in the 3rd quadrant, (equation of an imaginary circle)).
All the other equations are just reflections of this equation in all the other quadrants, thus the overall figure of all the equations would be a circle, touching 2 hyperbolas, where one has a vertical axis and the other horizontal. The hyperbolas will never intersect, and thus would never form a closed figure.
Thus, all we have left is the circle.
Area = π (1)² = π