
Applications of Integration 15-11
Area of Region Bounded by a Plane Curve in Polar Coordinates
Let r = f(q) be a polar curve and OP and OQ be two radii vectors which make angles a and b with
polar axis, respectively as shown in Fig. 15.6. Then we are required to find the area bounded by the
curve and the two radii vectors OP and OQ, i.e. the area OPQ is also called sectorial area of the curve.
Before finding the area, recall that if R, S be any two points on a circle with radius r (as in Fig. 15.7)
and centre at the origin and q is the angle between R and S, then the sectorial area ORS is given as,
Area ORS radius arc= = =
1
1
1
2
( ) ( ) (