   Chapter 8.6, Problem 33E

Chapter
Section
Textbook Problem

Estimating Errors Using Technology In Exercises 33 and 34, use a computer algebra system and the error formulas to find n such that the error in the approximation of the definite integral is less than or equal to 0.00001 using (a) the Trapezoidal Rule and (b) Simpson’s Rule. ∫ 0 1 tan x 2   d x

(a)

To determine

To calculate: The value of n for which the error in the approximation of the definite integral for the function f(x)=tan(x2) is less than or equal to 0.00001 using Trapezoidal rule using computer algebra system.

Explanation

Given:

f(x)=tan(x2)

Formula used:

The error (E) in approximating abf(x)dx using the Trapezoidal rule is,

|E|(ba)312n2[max|f(x)|], axb

Calculation:

To differentiate the provided function with the help of maple use the following command,

>diff(sec2(x),[x\$2])

Thus the output is:

4sec(x)2tan(x)2+2sec

(b)

To determine

To calculate: The value of n for which the error in the approximation of the definite integral for the function f(x)=tan(x2) is less than or equal to 0.00001 using Simpson’s rule using computer algebra system.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

A sample of n = 9 scores has X = 108. What is the sample mean?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Fill in the blanks. 8. a. The general form of an equation of a line is_______.

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In problems 15-26, evaluate each expression. 24.

Mathematical Applications for the Management, Life, and Social Sciences

Test for divisibility by 2: 877,778

Elementary Technical Mathematics 