Chapter 8.6, Problem 34E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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 2 ( x + 1 ) 2 / 3   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)=(x+1)23 is less than or equal to 0.00001 using Trapezoidal rule using computer algebra system.

Explanation

Given:

f(x)=(x+1)23

Formula used:

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

|E|â‰¤(bâˆ’a)312n2[max|fâ€²â€²(x)|],Â aâ‰¤xâ‰¤b

Calculation:

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

>diff((x+1)23,[x\$2])

Thus, the output is:

âˆ’29(x+1)43

Which lies in [0,2]

(b)

To determine

To calculate: The value of n for which the error in the approximation of the definite integral is less than or equal to 0.00001 using Simpson’s rule using computer algebra system.

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