Question
Sketch the region bounded by the curves 
and find its area using integration.
Solution
Consider the given equation. 
This equation represents a semicircle with centre at the origin and radius = 
Given that the region is bounded by the above semicircle and the line 
Let us find the point of intersection of the given curve meets the line 
Squaring both the sides, we have,
Consider the following figure
Thus the intersection points are 1,2 and 2,1 ( ) ( ) Consider the following sketch of the bounded region.
Required Area, 
