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Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
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Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
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Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
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Calculus I
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Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
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15.Functions of Several Variables
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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:

• 5.4.1 Approximate a definite integral using the Trapezoid Rule
• 5.4.2 Approximate a definite integral using Simpson's Rule
• 5.4.3 Use the appropriate formula to find the error associated with the Trapezoid Rule
• 5.4.4 Use the appropriate formula to find the error associated with Simpson's Rule
• 5.4.5 Evaluate a definite integral electronically

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)