## 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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**Example 6**

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

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**Example 4**

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

**Example 3**

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

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

**Problem**

Find the area enclosed by

• *r* = 2*a* sin^{2} θ

• *r* = 2*a* cos^{2} θ

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Apply Pythagorean theorem to the triangular strip shown in the figure:

$(ds)^2 = (dx)^2 + (dy)^2$ ← Equation (1)

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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.

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