RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 21. Areas of Bounded Regions

Subject: Maths - Class 12th

Q. No. 14 of MCQ

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14

The area of the region is

We need to determine what region is being talked about.


x2 + y2 = 1 is a circle with centre at origin and unit radius.


So, x2 + y2 ≤ 1 represents the region inside that circle.


x + y = 1 is a line that intersects the 2 axes at unit distances from the origin, in the positive direction.


So x + y ≥ 1 represents all the points, i.e., the region above the line x + y = 1.




So, the region {(x, y): x2 + y2 ≤ 1 ≤ x + y} is –



For each point (x, y) on circle in first quadrant, y = √(1 – x2)


For each point (x, y) on line, y = 1 – x


So, area A of the region described is –


A =


=


= π/4 – 1/2 (Ans)

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