How large should n be to guarantee that the Trapezoidal Rule approximation to3L - xª + 8x³ − 18x² + 3x − 3) dx is accurate to within 0.0001.n =How large should n be to guarantee that the Simpsons Rule approximation to3Ln=4- xª + 8x³ − 18x² + 3x − 3) do is accurate to within 0.0001.

Answered: How large should n be to guarantee that…

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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Question

How large should n be to guarantee that the Trapezoidal Rule approximation to
3
L - xª + 8x³ − 18x² + 3x − 3) dx is accurate to within 0.0001.
n =
How large should n be to guarantee that the Simpsons Rule approximation to
3
L
n=
4
- xª + 8x³ − 18x² + 3x − 3) do is accurate to within 0.0001.

Expert Solution

Step 1: Given.

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Given: $f (x) = - x^{4} + 8 x^{3} - 18 x^{2} + 3 x - 3$ , $a = 1, and b = 3$ .

To find: How large should be the value of $n$ which guarantee that the Trapezoidal rule approximation to $\int_{1}^{3} (- x^{4} + 8 x^{3} - 18 x^{2} + 3 x - 3) d x$ is accurate to within $0.0001$ .