Question

The area of the region R=\(x,y): |x|≤ |y| and x²+y²≤ 1 is

• A. (3π)/(8) sq units
• B. (5π)/(8) sq units
• C. (π)/(2) sq units
• D. (π)/(8) sq unit

Hint:

Convert inequalities to angular regions in polar coordinates.

Answer 1

The Correct Option is A

The condition |x|≤ |y| corresponds to angles between θ=(π)/(4) to (3π)/(4) and similarly in all four quadrants. Total angular region: 4((π)/(4))=π Area inside unit circle: (π)/(2π)× π = (3π)/(8)