Lecture 21 : Area between two curves [Section 21.2]
21.2.8
Remark:
(i)
As in Cartesian coordinates, in most of the area computation problems determining the limits of integration is
the hardest part. The following steps are useful for this:
Step 1: Sketch the region whose area is to be determined.
Step 2: Draw a radial line from the pole passing through the region. Find the length of the segment inside this region.
Step 3: To find the limits of integration, rotate the radial line around the pole in anticlockwise direction to find the
lower limit , where the radial line starts intersecting, till , when it stops intersecting the region.
(ii)
The area of a more general planer regions can be defined using the notion of double integrals in such a way
that is consistent with the formulae given above. This will be done in a later module no 14.
PRACTICE EXERCISES
1.
Find the area of the region bounded by the given curves in each of the following case:
, where the radial line starts intersecting, till 
, when it stops intersecting the region. 
