Math, asked by kaur4119, 11 months ago

How do you find the region inside cardioid r=1+cos(θ) and outside the circle r=3cos(θ)?

Answers

Answered by ritesh275
2

Find the intersection points of the curves hence we have that

3

cos

θ

=

1

+

cos

θ

cos

θ

=

1

2

θ

=

±

π

3

The saded area is

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

The cardiod area is

π

π

3

1

2

(

1

+

cos

θ

)

2

d

θ

=

π

2

9

6

3

and the circle area is

π

2

π

3

1

2

(

3

cos

θ

)

2

d

θ

=

(

3

π

8

)

9

16

3

Hence the shaded area is

π

8

The total amount is

2

π

8

=

π

4

A graph for the curves is

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