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Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
Course: Calculus II
Topic: Transcendental Functions
Subtopic: Numeric and Electronic Integration

Overview

Recall approximating the area under a curve by drawing rectangles and summing their area. The act of using rectangles caused some error in the area approximation which could be reduced by using a shape where the top of the strip more closely matched the curve such as a perhaps a slanty line (which would make the rectangles into trapezoids). This is the idea behind the Trapezoid Rule and Simpson's Rule, both methods of numeric integration.

These rules are particular useful for approximating definite integrals that cannot be evaluated algebraically. Of course such integrals can be evaluated fairly accurately electronically. This is a good time to practice integrating electronically (using a handheld calculator, an online integrator, or math computing software).

Objectives

By the end of this topic you should know and be prepared to be tested on:

Terminology

Define: trapezoid rule, Simpson's rule, error formula

Supplemental Resources (required!)

You must be able to use a calculator (handheld or software) to integrate a function. Integrating electronically is a good way to check your work. If you have a handheld graphing calculator then these sites may help:

Supplemental Resources (optional)

Video: Numerical Integration, Selwyn Hollis's Video Calculus

Lesson: Approximating Definite Integrals, Dale Hoffman's Contemporary Calculus