Home >> PURE MATHS, Integration, the trapezium rule

Theory & Method

The Trapezium Rule is a method of finding the approximate value of an integral between two limits.

The area involved is divided up into a number of parallel strips of equal width.

Each area is considered to be a trapezium(trapezoid).

If there are n vertical strips then there are n+1 vertical lines(ordinates) bounding them.

The limits of the integral are between a and b, and each vertical line has length y₁ y₂ y₃... y_n+1

width of each strip

area of first strip = (width of strip) x (av. length of 1st. and 2nd. verticals)

Therefore in terms of the all the vertical strips, while the actual integral is given by:

the approx. integral is

       = (strip width) x [(av. of 1st. and last y-values) + (the sum of all y values between the                                                                        second and second-last value)]

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Example #1

using a strip width of        

evaluate        

(answer to 2 d.p.)        

using approx. integral= (strip width) x [(av. of 1st. and last y-values)

+ (the sum of all y values between the second and second-last value)]

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Example #2

using a strip width of  '1' unit

evaluate       

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