Question

find by double integration the area which lie inside the cardioid r=1+cos(thetta) and outside the circle r=1​

Answer 1

Answer:

It is π4

Explanation:

Find the intersection points of the curves hence we have that

3cosθ=1+cosθ⇒cosθ=12⇒θ=±π3

The saded area is

(cardiod area from pi/3 to pi)-(cricle area from pi/3 to pi/2)

The cardiod area is

∫ππ312⋅(1+cosθ)2dθ=π2−96⋅√3

and the circle area is

∫π2π312⋅(3⋅cosθ)2dθ=(3π8)−916⋅√3

Hence the shaded area is π8

The total amount is 2π8=π4

A graph for the curves is

Step-by-step explanation:

hoping it would work out!!!