The most important rule, in practice, is the Simpson’s Rule, because of its simplicity and accuracy. When more accuracy is required, this rule should be used.

To find the area as shown in figure, the base must be divided into an even number of strips of equal width , producing an odd number of ordinates. The length of each ordinate is accurately measured. The first and the last ordinates are called extreme ordinates; second, fourth, sixth, etc., the even ordinates; and third, fifth, seventh, etc. are odd ordinates.

By Simpson’s Rule, the area is determined as:

Area

Where Sum of the first and the last ordinate

Sum of odd ordinates

Sum of even ordinates

Width of each strip

**Note: **This rule is applicable only when there will be an even number of strips or odd number of ordinates.

__Example__:

Find the area of an irregular figure whose ordinates are, , , , , , and respectively. The width of each strip is m.

__Solution__:

** **Since, the number of ordinates is odd; therefore, we use Simpson’s Rule

Area

Here m

Area

Square meter.

__Example__:

A parabolic piece of card board from root to tip m long. At equidistant places, the widths are: , , , , , , , and m. Find out its area.

__Solution__:

** **Since, the Simpson’s Rule is

Area

Here m

Area

Square meter.