The Trapezium Rule

It's only fair to share...Share on FacebookTweet about this on TwitterPin on PinterestShare on Google+Share on RedditEmail this to someone

The trapezium rule is a numerical method for estimating integrals. It is most useful when there is no analytical answer to an integral, and only a number is needed. It works by approximating the area under the curve by a series of trapezia, then evaluating the areas and adding them up.

The area under the curve is approximated by a series of trapezia.

The formula for the integral rule iswhereis the step size or the increment by which the values ofincrease, 1 in the diagram above andis defined byeg

For ease of calculation it is a good idea to tabulate the values of the

0

1

2

3

4

5

6

0

1

2

3

4

5

6

0

5

8

9

8

5

0

This estimate is an underestimate for the integral. The curve is concave – it curves down. In general the trapezium method gives an underestimate for the integral of concave functions and an overestimate for convex functions, an example of which is given below.

Comments are closed.