The trapezium rule is a method of finding the approximate value of the value of an integral between certain limits. In other words the trapezium rule is a way of calculating the area under the curve on a graph. You must know that an integration gives the area under a curve on a graph. The following is the trapezium rule.
…where h is the height of the trapeziums or the x values interval. And the ys values are the y values at the end of each strip as shown below.
The trapezium rule takes advantage of the are of a trapezium formula:
The rule works by splitting the area under a curve into a number of trapeziums we could find the area for. For example consider the graph in the following diagram,
The area below the graph curve has been split into a number of trapeziums. These trapeziums have been noted by letters A, B, C, and D
Find the area between the x-axis and the curve y = x2 + 2 between x = 1 and x = 5 using the trapezium rule with 4 strips.
First let’s draw a table to find out the y values.
So now we can use the trapezium rule. The trapezium rule states that as above:
The h is the height of the trapeziums or very simply the intervals between the x values. In the above table we have x values ranging from: 1, 2, 3, 4, and 5 The distance between these values is 1
The answer for the area between the curve of y = x2 + 2 is 50 square units
And that’s how you work with the trapezium rule.