# Polar Curves

## 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*.

## 01 Area Enclosed by r = 2a sin^2 θ

**Example 1**

Find the area enclosed by *r* = 2*a* sin^{2} θ.

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## 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...

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