## 05 Area Enclosed by r = a sin 2θ and r = a cos 2θ

**Problem**

Find the area bounded by $r = a \sin 2\theta$ and $r = a \cos 2\theta$.

## 06 Area within the curve r^2 = 16 cos θ

**Example 6**

What is the area within the curve *r*^{2} = 16 cos θ?

- Read more about 06 Area within the curve r^2 = 16 cos θ
- Log in to post comments

## 04 Area of the Inner Loop of the Limacon r = a(1 + 2 cos θ)

**Example 4**

Find the area of the inner loop of the limacon *r* = *a*(1 + 2 cos θ).

## 03 Area inside the cardioid r = a(1 + cos θ) but outside the circle r = a

**Example 3**

Find the area inside the cardioid *r* = *a*(1 + cos θ) but outside the circle *r* = *a*.

## 03 Area Enclosed by Cardioids: r = a(1 + sin θ); r = a(1 - sin θ), r = a(1 + cos θ), r = a(1 - cos θ)

**Problem**

Find the area individually enclosed by the following Cardioids:

(A) $r = a(1 - \cos \theta)$

(B) $r = a(1 + \cos \theta)$

(C) $r = a(1 - \sin \theta)$

(D) $r = a(1 + \sin \theta)$

## 02 Area Bounded by the Lemniscate of Bernoulli r^2 = a^2 cos 2θ

**Example 2**

Find the area bounded by the lemniscate of Bernoulli r^{2} = a^{2} cos 2θ.

## Plane Areas

## Plane Areas in Rectangular Coordinates

There are two methods for finding the area bounded by curves in rectangular coordinates. These are...

- by using a horizontal element (called strip) of area, and
- by using a vertical strip of area.

The strip is in the form of a rectangle with area equal to length × width, with width equal to the **differential element**. To find the total area enclosed by specified curves, it is necessary to sum up a series of rectangles defined by the strip.

- Read more about Plane Areas
- Log in to post comments