## 4.6 Trapezoid Rule

### Summary

Many applications of calculus involve definite integrals. If it is possible to find an antiderivative for the integrand, then the integral can be evaluated using the Fundamental Theorem. When an antiderivative is not apparent, numerical (approximate) methods are invoked. The numerical method that is discussed in this section is called the Trapezoid Rule.

By the end of your studying, you should know:

• The trapezoid rule formula.
• How to apply the trapezoid rule by hand.
• How to apply the trapezoid rule with an applet.

On-screen applet instructions: The applet illustrates the Trapezoid Rule. Select the number of subintervals from the pull-down menu. For comparison, you can click the buttons at the bottom to see other approximations.

### Examples

Approximate

with 4 trapezoids. Sketch a figure showing the curve and the trapezoids involved. Compare your answer with the answer you find using integration formulas.

Compare the 5-subinterval trapezoid approximation of

with the exact value of the integral. How great is the difference between them?

How accurate is the Trapezoid Rule for approximating integrals?

### Applets

Numerical Integration

### Videos

See short videos of worked problems for this section.

### Exercises

See Exercises for 4.6 Trapezoid Rule (PDF).

Work online to solve the exercises for this section, or for any other section of the textbook.

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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel