Chapter 5: Q. 5 (page 494)

The error $|E (n)|$ of an approximation of a definite integral by a Riemann sum.

Short Answer

Expert verified

$| E (n) | = |\int_{a}^{b} f (x) d x - \sum_{k = 1}^{n} f (x_{k}^{*}) ∆ x|$

Step by step solution

Step 1. Basics

We know that absolute value of the error for the approximation is as follow:
$error = |actual value - approximated value|$

Step 2. Final Answer

The error $|E (n)|$ incurred by using a given n-rectangle Riemann sum is the difference between the actual area and the approximated area:

$| E (n) | = |\int_{a}^{b} f (x) d x - \sum_{k = 1}^{n} f (x_{k}^{*}) ∆ x|$

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The error $|E (n)|$ of an approximation of a definite integral by a Riemann sum.

Short Answer

Step by step solution

Step 1. Basics

Step 2. Final Answer

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The error Enof an approximation of a definite integral by a Riemann sum.

Short Answer

Step by step solution

Step 1. Basics

Step 2. Final Answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Statistics

Mechanics Maths

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

The error $|E (n)|$ of an approximation of a definite integral by a Riemann sum.