## 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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**Example 1**

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

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**Example 3**

Find the area bounded by the curve *x* = *y*^{2} + 2*y* and the line *x* = 3.

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**Example 2**

Find the area bounded by the curve *a*^{2} *y* = *x*^{3}, the *x*-axis and the line *x* = 2*a*.

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**Example 1**

Find the area bounded by the curve *y* = 9 - *x*^{2} and the *x*-axis.

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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.