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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.
The trapezium rule takes advantage of the are of a trapezium formula:
Area of trapezium = h(a + b)/2
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,
Graph split into trapeziums
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
Trapezium rule Examples
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./
Explanation 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:
Area = h/2(y0 + y4 + 2(y1 + y2 + y3))
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
Area = 1/2(3 + 27 + 2(6 + 11 + 18))
= 50 square units
The answer for the area between the curve of y = x2 + 2 is 50 square units
Worksheets recommended by system:
Learn more about this topic in the following pages.