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In estimating involved in the approximation using the Error Bound formulas. For Trapezoidal rule, the error will be less than co cos(3x) dx using Trapezoidal and Simpson's rule with n = 10, we can estimate the error For Simpson's rule, the error will be less than Give your answers accurate to at least 2 decimal places

In estimating involved in the approximation using the Error Bound formulas. For Trapezoidal rule, the error will be less than co cos(3x) dx using Trapezoidal and Simpson's rule with n = 10, we can estimate the error For Simpson's rule, the error will be less than Give your answers accurate to at least 2 decimal places

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In estimating the integral \( \int_{-1}^{4} \cos(3x) \, dx \) using the Trapezoidal and Simpson's rule with \( n = 10 \), we can estimate the error involved in the approximation using the Error Bound formulas. - For the Trapezoidal rule, the error will be less than: [Textbox provided] - For Simpson's rule, the error will be less than: [Textbox provided] Give your answers accurate to at least 2 decimal places.
Transcribed Image Text:In estimating the integral \( \int_{-1}^{4} \cos(3x) \, dx \) using the Trapezoidal and Simpson's rule with \( n = 10 \), we can estimate the error involved in the approximation using the Error Bound formulas. - For the Trapezoidal rule, the error will be less than: [Textbox provided] - For Simpson's rule, the error will be less than: [Textbox provided] Give your answers accurate to at least 2 decimal places.
Expert Solution
Step 1: Description of given data

We have, integral subscript negative 1 end subscript superscript 4 cos left parenthesis 3 x right parenthesis d x, with n equals 4

Approximate the errors bound by using:

Trapezoidal rule

Simpson's rule

Let f left parenthesis x right parenthesis equals cos open parentheses 3 x close parentheses

Find its derivatives up to 4 orders

f apostrophe left parenthesis x right parenthesis equals negative 3 sin open parentheses 3 x close parentheses

f apostrophe apostrophe left parenthesis x right parenthesis equals negative 9 cos open parentheses 3 x close parentheses

f apostrophe apostrophe apostrophe left parenthesis x right parenthesis equals 27 sin open parentheses 3 x close parentheses

f to the power of i v end exponent left parenthesis x right parenthesis equals 81 cos open parentheses 3 x close parentheses

Here, a equals negative 1 comma space b equals 4 comma space n equals 4

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