Q. 5 The error En聽of an approximatio... [FREE SOLUTION]

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

$| E (n) | = |{鈭�}_{a}^{b} f (x) d x - {鈭�}_{k = 1}^{n} f (x_{k}^{*}) 鈭� x|$

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:

$| E (n) | = |{鈭�}_{a}^{b} f (x) d x - {鈭�}_{k = 1}^{n} f (x_{k}^{*}) 鈭� x|$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Probability and Statistics

Mechanics Maths

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

91影视

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

Statistics

Pure Maths

Probability and Statistics

Mechanics Maths

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

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