# limits of integration

**Problem**

Evaluate $\displaystyle \int_0^1 \dfrac{x \, dx}{x^2 + 2}$.

A. 0.2027 | C. 0.2270 |

B. 0.2207 | D. 0.2072 |

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## Example 6 | Plane Areas in Rectangular Coordinates

**Example 6**

Find each of the two areas bounded by the curves *y* = *x*^{3} - 4*x* and *y* = *x*^{2} + 2*x*.

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## Example 3 | Plane Areas in Rectangular Coordinates

**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 | Plane Areas in Rectangular Coordinates

**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 | Plane Areas in Rectangular Coordinates

**Example 1**

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

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## Plane Areas in Rectangular Coordinates | Applications of Integration

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.

### Using Horizontal Strip

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