# Integration of Polar Area

## 06 Area Within the Curve r^2 = 16 cos θ

**Example 6**

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

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## 05 Area Enclosed by Four-Leaved Rose r = a cos 2θ

Find the area enclosed by four-leaved rose r = a cos 2θ.

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## 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*.

## 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 in Polar Coordinates | Applications of Integration

The fundamental equation for finding the area enclosed by a curve whose equation is in polar coordinates is...

$\displaystyle A = \frac{1}{2}{\int_{\theta_1}^{\theta_2}} r^2 \, d\theta$