Question

1.Find, by double integration, the area of the lemniscate r²=a²cos2.
2.Find, by double integration, the area lying inside the circle r = a sin 0 and outside the cardioidr=a(1-cos)
(Andhra., 2015; Rohtak, 2012; PT.U
3.Find the area lying inside the cardioid r = 1 + cos and outside the parabolar (1 + cos ) = 1.
4.Find the area common to the circles r = a cos , r = a sin by double integration. ​

Answer 1

Answer:

Double integration in polar coordinates. 1. 1. Compute. R f(x, y) dx dy, where f(x, ... (inner) r from 0 to 2 cos θ; (outer) θ from −π/2 to π/2. ... 2. Find the area inside the cardioid r = 1 + cos θ.