Sketch the region bounded by the curves and find its area using integration.
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,