# Simpson's Rule

The most important rule in practice is 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 the 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 the extreme ordinates; the second, fourth, sixth, etc., the even ordinates; and the third, fifth, seventh, etc. are the odd ordinates.

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

Area

Where sum of the first and the last ordinate

sum of the odd ordinates

sum of the even ordinates

width of each strip

**Note: **This rule is applicable only when there is 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 meters.

__Example__:

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

__Solution__:

** **Since the Simpson’s Rule is

Area

Here m

Area

square meters.