Unit 6 - Objective 1 - Trapezoidal Rule




The Trapezoidal Rule is a way to approximate the definite integral. This is useful because all functions do NOT have antiderivatives, and all shapes do not have functions to represent them. The Trapezoidal Rule, which uses area of trapezoids, is a much better approximation than rectangles.




To approximate

Solution: From the integral above we can read the following.











The Trapezoidal Rule can be used to estimate an integral, or area, even when there is no function to represent the curve.


Find the integral (area) of one side of a small machined plate where the heights of the plate have been measured at regular intervals and recorded in the table below.


x00.51.0 1.52.02.5
h2.1 cm2.3 cm2.2 cm 1.0 cm0.8 cm0.6 cm



Now according to the Trapezoidal Rule the area of this plate, or the integral, is


NOTE: For the Trapezoidal Rule, the pattern of the coefficients is: 1 2 2 2 2 ... 2 2 1


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