## Evaluate the integral of (x dx) / (x^2 + 2) with lower limit of 0 and upper limit of 1

**Problem**

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

A. 0.2027 | C. 0.2270 |

B. 0.2207 | D. 0.2072 |

**Problem**

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

A. 0.2027 | C. 0.2270 |

B. 0.2207 | D. 0.2072 |

**Example 6**

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

**Example 3**

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

**Example 2**

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

**Example 1**

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

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.