Problems of this kind are variable and each one may demand a different approach.
In the diagram belowis the curve
and
is the curve
W e have to find the shaded are and this must be done in several stages.
We find the points A and B of intersection of the two curves, specifically, we find thevalues
and
Having found these, the shaded area will consist of the sum of two integrals:
We integrate forthe cardioid between
and
and for
between
and
Notice that
is negative.
The pints of intersections are the solutions to
Forwe integrate between
and
or anticlockwise from
The area of the circle between A and B is
The shaded area is the sum of these