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# Formulae

DOI link for Formulae

Formulae book

# Formulae

DOI link for Formulae

Formulae book

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## ABSTRACT

Simpsons Rule The Area is divided into an even number of strips of equal width, and therefore has an odd number of ordinates at the division points

area = SðAþ 2Bþ 4CÞ

where S = common interval (strip width) A = sum of ﬁrst and last ordinates B = sum of remaining odd ordinates C = sum of the even ordinates

The Volume can be calculated by the same formula, but by substituting the area of each coordinate rather than its length

Trapezoidal Rule A given trench is divided into two equal sections, giving three ordinates, the ﬁrst, the middle and the last

volume = S ðAþ Bþ 2CÞ

where S = width of the strips A = area of the ﬁrst section B = area of the last section C = area of the rest of the sections

Prismoidal Rule A given trench is divided into two equal sections, giving three ordinates, the ﬁrst, the middle and the last

volume = L ðAþ 4Bþ CÞ

where L = total length of trench A = area of the ﬁrst section B = area of the middle section C = area of the last section