Integration: The Trapezium Rule

[ method ][ example#1 ][ example#2 ]





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.

trapezium rule diagram#1

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... yn+1

trapezium rule theory#2

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

trapezium theory


approx. integral = (strip width) x (average of first and last y-values, plus the sum of all y values between the second and second-last value)


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Example #1

trapezium rule problem#1


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Example #2

trapezium problem#2




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