Q34 of 36 Page 1

Using integration, find the area of the region {(x,y) : x2 + y2 1, x + y 1, x 0 , y 0 }

Given: {(x,y) : x2 + y2 1, x + y 1, x 0 , y 0 }


To Find: Area of the enclosed region.


x2 + y2 1 means the area enclosed inside the circle of radius 1 and centre at (0, 0)



Now, x + y 1 is drawn, which indicates the area opposite to the origin.



We need to find the area enclosed by the AB straight line and C circle.


Therefore,


Required area = Area of ACBO semi-circle – Area of ABO triangle.


x2 + y2 = 1


⇒ y =


So, the area =


=


= unit2


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