Estimate the minimum number of subintervals needed to approximate the value ofa. the Trapezoidal Rule.b. Simpson's Rule.5- 54(5x² + 7) dx with an error of magnitude less than 2× 10by

Given :Interval is from -5 to 5error of magnitude is less than Use the error estimate formula for…

Answered: Estimate the minimum number of…

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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Related questions

Question

Estimate the minimum number of subintervals needed to approximate the value of
a. the Trapezoidal Rule.
b. Simpson's Rule.
5
- 5
4
(5x² + 7) dx with an error of magnitude less than 2× 10
by

Expert Solution

Step 1: Information

Given :

$integral subscript negative 5 end subscript superscript 5 left parenthesis 5 x squared plus 7 right parenthesis space d x$

Interval is from -5 to 5

error of magnitude is less than $2 times 10 to the power of negative 4 end exponent$

Use the error estimate formula for the Trapezoidal Rule

$vertical line E subscript r vertical line less or equal than fraction numerator left parenthesis b minus a right parenthesis cubed over denominator 12 n squared end fraction open parentheses m a x vertical line f apostrophe apostrophe left parenthesis x right parenthesis vertical line close parentheses$

Now take derivative for $5 x squared plus 7$ .