Question

Find the area of the region included between the cantinids r= a(1+ cos theta) and r = a(1- cos theta).​

Answer 1

Step-by-step explanation:

The cardioid r=a(1+cosθ) is ABCOB′A and the cardioid  r=a(1−cosθ) is OC′BA′B′O

Both the cardioids are symmetrical about the initial line OX and intersect at B and B′

∴ Required Area=2Area OC′BCO

                     =2[areaOC′BO+areaOBCO]

                    =2[(∫02π21r2dθ)r=a(1−cosθ)+∫2ππ((1+cosθ)2dθ)r=a(1+cosθ)]

              =a2[∫02π(1−2cosθ+cos2θ)dθ+∫2ππ(1